Shutting off for power when fully charged?

[jgsugden]

My droid is doing something odd: When fully charged (and sometimes when on the charger and fully charged), the red light blinks, the battery suddenly shows as empty and the phone shuts itself off. My wife's phone is doing the same thing, but less often. We bought the phones around the time they first became available - is anyone else having this problem? If so, what have you done about it?