why resign when only a piece down?

Quite often, people resign when only a piece down. I don't see the point. There is so much to play for and also I find when I'm down that my opponent is often slightly vulnerable as the position can be a little unbalanced. They may also get a bit complacent. While it gives me a fair number of easy wins, I really think that people should rethink these early resignations. I think Tartakower said that a resignation never led to a win.

well if i lose my queen and they still have theirs i usually resign. but thats because im a bad player.

I'd say it's never worth resigning at your level regardless of point difference. If you genuinely don't have a hope, then just try to force a stalemate. Playing from a worse position will improve your game if nothing else because you'll be forced to try and set up traps to regain the material or force a draw.

Here's a game I just played where I was only a pawn down, but with a 10 point disadvantage.

White blundered by making a careless move and so I was able to force a draw.

en.lichess.org/RyYnx55b/black#0

I generally enjoy to play at bad positions trying to practice my defense and endgame skills.

Some players resign because they over-estimate my attacks.
In this game:
en.lichess.org/xwjhaibh1bNn
my opponent missed 8...fxe5 catching the dangerous knight in the explosion and avoiding the checkmate.

At lower levels of chess, resigning should rarely be on your mind. It is all too common that after one player blunders, losing a piece, their opponent soon returns the favor. At higher levels of chess, as in 1900+ players, it is far too unlikely that a player will outright blunder a piece, or that their opponent will do the same in kind. Therefore, since it is almost certain that, with their overall move accuracy and your obvious disadvantage, you will not win the game down a piece, resignation ensures that no one's time is wasted and the you can work towards regaining your lost points in another game rather than having spent 30 extra minutes playing a lost position because you're too stubborn to resign.

@Asym
At highest level of chess, during the 2014 world championship match, Carlsen blundered and Anand returned the favour in the next move.
en.chessbase.com/post/sochi-g6-carlsen-won-anand-missed-big-chance
http://www.chessgames.com/perl/chessgame?gid=1778864
The moves are: 26. Kd2? a4?
You are right though if the game is against a strong chess computer engine. In a game between two humans, everything can happen.

watch chessbrah video, when all the games he (eric hansen) sac the queen for nothing and win all the games.. awesome games!

One of the greatest game I've ever played was when I lost my queen early in the game. I didn't give up, but instead chose to take my time and over analyse every little weakness my opponent had throughout the rest of the game. Coordinating my pieces to the fullest potential, I ended up outsmarting him and got his queen, and eventually won the game. It wasn't because he made really big mistakes too, I was David against Goliath, and vanquished because I was determined to win. You never know what will happen, and you should treat every position with the belief that somewhere lies victory, no matter how impossible it might seem.

The thing is that at strong players simply switch gears when up a piece, just simply consolidate the position and then trade everything down into a simple endgame. Most mistakes in GM games occur in complicated positions where material is balanced or where there is some material imbalance with some compensation.