The way I see it, if you didn't make any mistakes in a game, you cannot lose it. I would continue to suffer for a few more moves to punish myself for making mistakes and hope not to make them again. Seriously, resign too early takes away some fun of playing chess. You enjoy a winning position, why not feel the other way as well.
I know when I am losing!
If you're just playing for fun, then you can resign whenever you want. (And your opponent doesn't need to "accept" it.) Sometimes it's better just to move on to the next game than to keep playing in a dead lost position.
A lot of people ask me: "Why did you resign?" It's because I know that the game is lost. Unless I can see a way to really save the game I will save the two of us the trouble if you are willing to accept my resignation.