I'm just the opposite. I'll usually continue to play a game where I'm losing, trying to catch up. It's the games where I'm so strong that victory is a sure thing that I'm likely to abandon.
Try the current game of the month. Always war. Not fun, in my opinion. I was trying a practice game at a lower level with similar parameters. Eventually, wave, after wave, after wave of MULTIPLE opponents comes tromping through my area, killing off my preatorians. (Due to MULTIPLE attacks and some lucky dice rolls.) I give up.
Also, when I'm in third place on points, close to another space race victory, why bother?? If I'm lucky, I pull it out. Sometimes, they can pull it out a year or three ahead of you. OR, like a recent game, Mansa earns a diplo victory a YEAR before I'm done the space race. So, if I'm in a similar situation, I will not finish. Been there, done that.
BUT, my current game is not a "give up". I'm WAY behind in points. Somewhere just past about 500 AD. Monty attacked me and I am merrily killing him off. Then, Mansa declares on me and sends one small stack in. A couple of weeks ago, I might have made nice with Monty and went after Mansa. Today, I'm building up my preatorians in the north (to protect against another incursion), while my army in the south goes after Monty. Once I kill off Monty, I'll redirect all the hoards toward Mansa.
Here I'm trying to learn about playing a little more agressive game. This is fun.