First thing I'd try is to use Task Manager, kill all apps, and fully-charge overnight. Make sure you reach 95-100%.
If you still have problems, I'd try a reset to factory defaults.
You'll ahve to reload everything of course. I know there are apps like Titanium Backup for backing up data on your device. I don't think that you're going to get apps backed up and reloaded thought. Someone else with real knowledge of this should participate in the discussion; I am far from an expert.
You should not let the battery go to dead. These lithium ion batteries do not suffer from "topping up" like the old niCads. Keep it charged at work, home, car...whatever. Top it up every night.
My battery life has been fantastic. Wake the unit up at about 7:00 AM. Various fairly light email and general use most of the day. Calculator, checking Android Market, bit of browsing, check BBC, more email at lunch, play music for a couple of hours...and so forth all day. Maybe one day out of 5 engage Google Maps with navigation for a half-hour or so. At home, check email, watch netfilx for 2 hours, check email, listen to music for an hour...at 11:00 I would typically be between 20-35% after all that.
Sounds like time is running out on your return period so maybe just return the darned thing. Of course then you will really have to start from scratch. And most retailers won't just take it back; Best Buy wont. Their extended warranty was WAY too expensive. You have to ship back to the manufacturer and , of course, WAIT.