I guess there is always the fact that some people are more talented than others. But, I'd like to believe that hard work should be able take you a long way. If you keep training tactics you WILL eventually see them coming at you. As far as mindlessly hanging pieces I do that all the time, you just have to shake it off and keep on playing. If you lose because of it, shake the loss off and move on. Chess is as much mind set and personality as talent, if you honestly believe you can win that goes a long way. It sounds to me like you need to get the ideas of losing, stagnation, and blundering out of your head and push onwards.
Brutal opinions please: is it possible I am not capable of improving

It's possible that you don't have the mental capacity to play chess at a high level, but I wouldn't label it an 'intelligence' problem in any case.

You probably are quite good already. It is possible you need to train eyesight by studying the board better and making sure that you imprint the position of the pieces and their range better and deeper.

You have to practice the right thing: To force yourself to do a blundercheck every time! I'm pretty sure your strategical and tactical- knowledge is good enough but you sometimes feel like it's not necessary in this or that situation. 20 moves you can get away with it but on the 21th it happens: Bang, overlooked a pin or a Knight-fork and there goes your piece.
Being good at tactical calculation is of little use if you realize that it is something you could and should have done after your move instead of doing it.

You can improve. From what I've seen in Heisman's Improving Chess Thinker stronger players start off with a positional assessment, say who stands better, by how much, and why, then decide on candidate moves and analyze all of them. This includes blunder checking to ensure a move can't be refuted with some check, capture, or threat. Even some quiet moves can refute your plan (e.g., the opponent plays b3 after your intended Nb6-Nc4) but it's better to have a bad plan than no plan.
When you should plan or adjust your plan is:
When you're out of book
After a pawn move
A piece exchange.
When you calculate you need to calculate until the end of the forcing variations then make an assessment.

the problem is your thinking process..
my advice is always LOOK FOR CHECK! CAPTURE! THREAT! of your opponent before making your move! making a mistake is just fine because you will learn from them.. JUST ENJOY THE GAME. OK.

Possible, yes--but only you can answer if you are actually capable of improving. And don't think it has anything to do with your intelligence. Being good at chess means you're good at chess. Being bad at chess does not necessarily mean you lack intelligence--maybe in a certain area--but isn't that true of everyone?
I quit chess for a long time, for basically the same reason. Have I improved since coming back? Yes! Significantly in Online chess. I'm better at tactics, I've improved in my ability to calculate, though my skills are quite uneven still. But my games at faster time controls have not improved at all. I believe it is because I have accumulated years of bad chess habits, and they are extremely hard to eliminate. That's my theory anyway. Now I have to prove it.
But I've decided that above all, I'm just going to have fun. Chess is something I enjoy, whether or not I ever get any better, it's fun. I enjoy an interesting game and a brilliant tactical shot like I would enjoy a fine piece of music or a work of art. And if that's as far as it goes, that's fine with me. But it would be really cool to prove that I can get better, even substantially better! (Class A or NM.) And that keeps me motivated to improve. But if I don't, it's not the end of the world.
So stop putting so much pressure on yourself. Just have fun. And if it really isn't fun for you, don't do it anymore.
I've cataloged my journey in my blog. You might be interested: http://www.chess.com/blog/OldChessDog

In some of your games you moved a piece twice in the opening and fell behind in development. When you're behind in development you can sometimes find yourself in seemingly impossible tactical situations because you don't have enough pieces out to defend.
Sometimes when you have a lead in development you can get lucky and just happen to find some crazy move that works. Your opponents seem to be finding these opportunities. By developing all your pieces you will be able avoid these situations in the opening.
I also noticed that you only seem to do this when you're playing against 1.d4. When you played the open games (1.e4 e5) on either side you never seemed to do this. I would reccomend you try 1.d4 d5 2.c4 e6 as Black and go from there. Yes you are making two pawn moves in the opening but this is ok here. This way after cxd5 you can play exd5 and keep a pawn in the center.
Here are some tips in the opening: http://exeterchessclub.org.uk/content/ten-rules-opening
In one of your games you had an opportunity to beat your opponent quickly with a development advantage. I think it's a pretty good example of what to look out for.

If you hang your pieces you need to work on your decision making process; half the moves in a game of chess are made by your opponent. Looking for moves your opponent can play is as important as looking for moves you can play.
Try playing some games with a longer time control - two/three days.
Everyone drops pieces at bullet and during time scrambles.
If you still regularly drop pieces with longer time controls then it is my experience that you will improve with increasing experience but rather slowly - a year or five can go by w/o your noticing any change. Just every now and then you get to see that you have made some small advance or other.
If you want to advance more rapidly then maybe you should look for some other pastime.

Try a copy of Tactics Time. Fits in your purse or back pack and is just for casual players or people who do not have time to study.
Enjoy,... A copy of Tal's Best Games, by TAL or David Bronstein is pure enjoyment.
I know the feeling, ... at least at blitz.

Wow, the amount of responses is heartening! Thank you all. I did not expect much from this thread when I initially posted it.
Many suggested a different thinking process or other ways to notice blunders. Unfortunately, this isn't really feasible, or I would be doing it now. This is why I started the thread; I thought perhaps some people just aren't mentally capable of employing these processes.
TitanCG, thank you! I did not expect many responses to my post, let alone for someone to look through my games! You are correct that I have no clue how to play against the queen's gambit. And as for the game you analysed, that's an amazing trick! I knew his Queen move was a poor choice on his (her) part, but I just could not figure out how to capitalize on it. I'll try that combination in the future. I really, really like how, rather than tell me 'this move is better', you also explained how the move I chose wasn't a poor move in terms of reasoning, but that it was just inferior to another move. I remember that game, and I spent more time on that queen move than I would have prefered (still not much though).
I don't mean this in a bad way, but it is comforting to know that players who are better than I also hang pieces occasionally. It makes it feel much less like a brick wall of improvement and more like a process of blundering less over time. I think the frustration comes from consistently losing games not being able to use my study of the game due to blunders. On the one hand, yes, it is frustrating to lose. But much more uspetting, and this is where it really bothers me, is that I love the nuances to chess, the strategy, the game. I'm drawn to it, the same way I'm drawn to my hobbies, or fascinating sci-fi shows, or my wonderful partner (don't tell her I compared her to chess). I just like the game; it's like a part of me. But it seems pointless to study it, to truly enjoy it as a learning pasttime, and to read fascinating books about it, when I know I'll play my next game and drop a piece guaranteed.
I think several of you hit the nail on the head. Many of you said I can improve, it just may take a long time. I'm okay with that. In the meantime, perhaps you all had a wonderful idea about playing longer time control games. I think that should definitely help. When it comes to chess moves, I'm just terribly slow.

[...]
Many suggested a different thinking process or other ways to notice blunders. Unfortunately, this isn't really feasible, or I would be doing it now. This is why I started the thread; I thought perhaps some people just aren't mentally capable of employing these processes.
[...]
Why don't you think this is feasible? You should think of thought process as a skill. Learning how to think in chess is like learning any other skill, such as learning how to play guitar. You can read books about it but you won't actually improve until you start practicing the skill you want to improve at.

1) CHOOSE quieter openings.
Then you won't find yourself in crazy, wide-open, middlegames, where you apparently blunder too much.
2) STUDY a few good books.
3) LEARN to win your games (mostly) through pawn promotion.
P.S. leaving queens on the board leaves you open to a schocking reversal of fortunes. Learn to exchange pieces, and improve your endgame knowledge.
Lots of wins await you. VERY SIMPLE.
I've played chess for years. I've put many countless hours into actual study, both reading and application. I've trained tactics religiously. And I always drop pieces in a range from instant hanging to 3 move combinations. It was so frustrating I actually quit playing chess for over a year. So please be honest and give me your opinions: is it possible that I just do not have the mental capacity to ever stop blundering to anything less than 3-4 move combinations? Are there some people who just do not have the intelligence to improve beyond this base level of play, no matter the time or effort spent?