I do notice that in many master games usually end with one side resigning right before they get mated, or their opponent has a strong advantage. I always say lose with dignity! (unless you're really angry and resign out of anger.)

On the contrary there is some dignity in resigning when the loss is obvious.

It saves time and effort for both sides, and I don't think masters really care about attaining a checkmate anyway.

I am certainly no master, but what annoys me (sometimes) when a guy sticks in there to the bitter end no matter what.  I can see why you might think that you can luck into a stalemate in K+Q vs K, but sometimes its just ridiculous.  For a master, however, I think they respect their opponent enough to know that in a hopeless situation the opponent isn't going to screw it up.  Going past the point of complete hopelessness is pointless since the winner isn't going to screw up and the loser can't come out of the loss.  

Yeah.... I had this match at Jr. High Nationals last year in the last round where my opponent just sat there and waited for about 30 minutes, waiting for his time to run out. I finally told him:

" I am sorry to be rude, but I have a schedule to keep, so can you please resign or make your move?" (It was a mate in one.) He also offered a draw!

Wow.  That really sucks. What a loser.  I can't imagine what its like to be in your position, but I'd be tempted to pull out a novel and start reading it.  You could pull out a chess book, but then that might be against the rules or something.  

You could just sit there and stare at him.  Just stare for 15 minutes.  Or maybe say something like "I'm sorry but I find you very attractive.  While you are staring at utter defeat here, I'll just be undressing you with me eyes. "  OR look at how much time is on your clock and go grab a burger.  Be sure to be back before your time runs out.  That way the moron might abandon punishing you for winning and walk away.  haha.  

There have to be 100 other ways to screw with a guy like that.  

ugh.... body shaking.... so starving...... going to grab something to eat.

Imagine you was lucky playing a very strong GM in first round in a big tournement, with a system like that. Your playing in a BIG room, with journalists asking out the GMs and your proud to play a world class pro chessplayer. He destroys you completely, and soon he is a rook, a queen and a few pawns ahead. He is starting to get bored. Now would you resign?

If you resign you can talk about the game, and if you are lucky yo ucan go it through and he will teach you something. You can say "hi" if you meet again.
If you dont resign, you have wasted you boths time, and he will be a bit irritated(?), and you can forget everything about him teaching you something.

Economy of effort.  If you resign it gives you a chance to rest up for your next game. 

Or when they offer you a draw in a similar situation...

May be it would be better if you resign on the second move? Or on the 6th move? What is the convention by the way?

for a guess,maybeit is futile to continue as there are no counter chances to achieve  win draw or stalemate.why prolong the agony of losing anyway,my departed chess friend use to say. we must concede  defeat to the better chess player as a sign of goodsportmanship for this noble game.

Why do master chess players resign when they're about to lose?

Because they're about to lose.

resigning a lost position is a sign of respect for your oponent and yourself. 

 +1

If a GM gets into checkmate, it means he didn't see it coming.

Afraid I don't really understand the point you're trying to make.

lol...well, I really don't think you should be the one concerned about being rude here.

I liked the "undressing you with my eyes" suggestion.  You might also try singing (to the tune of "It's Beginning To Look a Lot Like Christmas"):  "It's beginning to look a lot like next round..."