Answer:
it could possibly be a rogue app running in the background.
check your battery stats (settings>battery) and see what is using the most battery. usually it is screen, then voice calls, then some android stuff. anything higher than that is the problem app (unless you are playing games and stuff)
but with the screen off, you shouldn't be loosing 50% in 30 minutes. maybe 5% at most.
also, download "CPU spy" for a couple days. use the phone for a day, then check it out. if you phone doesn't go into "deep sleep" then there is SOMETHING running in the background.
unfortunately, without rooting, i am not sure exactly how to pinpoint the problem app. i used Better Battery Stats from the XDA forums and was able to pinpoint my problem app when i was getting serious battery drain....but i am pretty sure it requires Root (its worth a shot checking out though)
it might also be a bad battery, but usually it wont just drop off like you described....bad batteries are more of a gradual degradation of battery life
