I also have had a T3 some time. I don't charge overnight, but leave it on about an hour to "fully charge." I don't think 15 minutes is enough - I laughed when I read "just leave on a few minutes" in the manual.
What you can try is this . . . use the battery til it's quite low. Place the T3 on the charger, and WHILE ON THE STAND, do a soft reset. Resetting the Palm ON the charger also resets the "charger memory." Take off the cradle, turn off, and replace on cradle and leave it a couple of hours. You should see a difference.
I've never condoned leaving them on all night but many people do. Rechargeables have so many "cycles" before they start to tire, but I seriously doubt you or any of us have exceeded that number, which is probably very high. The auto-shutoff prevents overcharging; my opinion is that also sometimes prevents a full charge unless it's "dedicated to charging" for a period of 1-2 hours without activity.
I've also noticed that when on charger, if you turn the unit on and use it, you're not actually charging, and the battery depletes a little despite being ON the charger; in that case I turn off, remove it, turn off, and replace on charger for an hour. I have not seen shorter life (yet) and use my T3 daily. I think doing the reset may solve your problem. Cheers! /p