This can happen following an update. I would suggest the following course of action to resolve (Apple will instruct you to restore if you speak to them also).
First, sync with iTunes so you have a backup.
Then perform a "restore" in iTunes. This will re-install fresh 4.3.3.
When the restore completes, allow the iPad to reconnect to iTunes. It will ask you to set up new or restore from backup.
Choose to restore from the backup you made before you started (do NOT set up as new)
Allow the restore to complete, and then let all your apps re-sync automatically. This process involves a restart of the iPad so don't interrupt it. Leave the iPad connected to iTunes throughout. It will take a while if you have a lot of content on your iPad!
See how you get on with this. It can often get rid of whatever is panicking in your current setup and causing the battery drain.