I too have been having this problem for a few weeks now. But I've also had the phone for a few months, and the battery life was great in the beginning. The degradation wasn't a gradual thing, it pretty much came on all at once. Pretty much overnight, the phone (on standby, screen off) started discharging at a rate more akin with talk time than standby time.
Push is off. I've turned off 3G and wifi, no help. I've learned how to "shut down" all open apps (double click home, tap&hold app icons, then close them one by one) but even after I do that,
and do a hard reset (hold both home and power buttons for a few seconds) and boot back up fresh, I still can't get enough battery life for the phone to last one day on standby, and the phone gets hot as it discharges, even just laying on the desk not being used.
Here's what I've also noticed: there's a "stutter". For example, if I open my contacts and scroll through them, the scrolling action is no longer smooth like it once was. It "locks" up about the rate of three times per second, at a pretty even rate. And when I'm in the phone app, the interface is unresponsive unless i keep tapping a certain button or recent call entry. So I really think my issue is related to a constantly working processor.
I guess I'm going to have to try a Restore before I head to the Apple Store. That scares me.