Sounds like a hardware issue. I suggest promptly replacing it with your carrier before your return grace period is up (30 days with AT&T, for example.) You will need to do this at the same store where you purchased the handset.
I have the exact same problem with my new Atrix. Unfortunately (for me) I unlocked its bootloader, so AT&T is refusing to honor the warranty. I sent it in to Motorola for repairs, but it's still doing the same thing (Moto was nice enough to re-lock the bootloader, but AT&T is still not budging.) In my case, I have a feeling that it's either damaged battery contacts on the phone, or perhaps a faulty battery itself. I am planning to send it to Motorola again (on their dime this time) to see if they can fix it for real this time.