The problem boils down to this, I think; I thrive best in the face of adversity, and all-too-often forget that my players don't.
When my characters are tested, when the mustache-twirling villain threatens things they hold dear, my automatic, instinctual response as a player is to fight back with a stubborn, never-say-die tenacity that would make John McClane proud. And unless I'm playing a particularily meek character, that's often the IC reaction as well. When the bomb begins counting down, I make knowledge rolls for which wire to cut instead of running for my life.
However, my gaming group reacts differently. Even the most minor of setbacks (ie; the caravan was damaged in the skirmish, you'll have to traverse the last mile of the Dark Forest on foot....and dusk is beginning to fall...) cause my players to react harshly, as if the universe is doling out unfair cosmic punishments at every turn, no matter how rarely these setbacks may take place. I'd rather not provide additional examples because they'd come out sounding quite whiney, which is not the tone I'm going for here at all.
So before I stray too far from the topic, allow me to repeat the subject line; what motivates your characters? I understand this varies greatly between games and the personality which you're roleplaying, but let's try for broad strokes here. Do you enjoy it most when each of your accomplishments are followed by a wave of applause and cheering? Do you, like me, game for the sense of accomplishment and victory against all odds? Do you find yourself best motivated by ingame wealth and character advancement? Power over NPCs, perhaps a political position or other prestigious advancement? Does the promise of combat to come get your blood pumping? Do you take risks and make deliberately bad choices 'just to see what will happen? Do you loathe one-sided, no-effort victories, or wish they could ALL be like that?
I would like to simply ask, 'How would you motivate a group of players that become discouraged at even small challenges?' but this seems far too difficult to answer without knowing the group on a personal level.