Note: You MUST read the 'How To Play' first. Seriously. Otherwise, you won't have a clue what's going on. If you're losing health inexplicably, it's either because your units are being killed, the enemy is using a catapult barrage on you (costs 'em 500 gold), or they've got an army and you haven't.
Enjoy. By the way, play it in Easy mode first. And yes, it is possible to win. You just need a good strategy. Try building the stronger units - they'll take longer to make, but they'll surivive longer, too.