It's funny how if I play somebody lower than me, they're considerably less likely to resign against me than a master in the same position. Waste of time.
People who DO NOT RESIGN in a lost position.

Surely nobody would resign against an 1143 player. Ever! Make them prove they actually understand how to checkmate!

So I'm supposed to assume my opponent will play like Magnus Carlsen every game rather than the low rated player he is?!

We're talking about whether you resign or not. That's not a question of playing your best, it's a question of deciding whether your opponent will convert their clear advantage or whether you think they will blunder and you can still win. So for that my opponent's rating (as well as other things) is an important factor. I'm not going to play on a Rook down against an 1800 player (unless it is Bullet), but against a 1200 player sure I'll carry on and force him/her to prove they know how to actually win, although there is a possibility I'd be so embarrassed at being a rook down against a 1200 player that I would just resign anyway.
After moves 14 and 15 from black in Joe-harpers' game, he deserved to lose.
it looks like he was TRYING to lose.

Well over the last few days, I've played a few games where somebody should have resigned and didn't and ended up winning. I think I shall never resign unless it's a one-move mate that's obvious. I was down a queen in one game and won when the guy blundered his queen.
Another guy refused to resign down five pawns and a bishop, so I queened all five pawns...it was really fun actually (I learned that from the guy above in this thread). I know the guy was hoping for a stalemate, which I've done stupidly plenty of times....but not recently. I really try and watch that at the end.
By the way, please help me with this...is a Glicko rating of 21 any good? Thanks in advance.
Even resigning when it's an obvious mate in one is sometimes only obvious to you, not to your opponent. A couple weeks ago I had a game where my opponent was up a queen and a bishop, had an obvious mate in one, and plenty of time. Instead he made a completely unexpected move, planning to mate on the next move. What he didn't see what that his move resulted in stalemate since he didnt notice my escape square was no longer usable.

It depends on your opponent. There are opponents who are sharp and there are opponents who blunder often. Sometimes I'm sharp. Sometimes I blunder a lot. On blitz it happens frequently. Against an opponent who show lack of focus, don't resign, even if you're a rook down.

To answer the author's questions, they're just probably prolonging the fun, waiting for you to make mistake or blunder, or just frustrating you. I haven't encountered one but I won't mind them (provided my tablet's battery status is OK).

I think playing the game until checkmate is a good learning experience for lower ranked players (so I don't resign a lot and I don't mind others who don't resign).

After moves 14 and 15 from black in Joe-harpers' game, he deserved to lose.
it looks like he was TRYING to lose.
Yeah, I did deserve to lose. It was her low rating that removed my guard. I didn't try to lose however, that is against the site rules and that game was for my team the Piece Munchers in the Not-So-Pro Chess League.

Everyone has a right to make their opponent beat them. Granted, it can be quite masochistic to play in a hopeless position, but I've won or drawn many games I shouldn't have that way. Furthermore, if anyone chat messages me telling me to resign, I won't. I view that request as rude and I punish it by persistence... and I often frustrate them and win.
Because nobody have ever won a chess game by resigning