Absolutely return the phone and get a new one! This is not normal behavior. I bought my Droid on day 1. On Sunday, after using it for a day and a half, I noticed rebooting and turning off. I had not installed anything. Took it back and requested a new one. Of course it worked fine in store, but I can't take a chance with phone not working. Sales rep tried to talk me out of it, but I insisted, and said Verizon has a 30 day return policy.
She opened the battery cover, removed the battery, and tried to give me some cr*p about the battery being overcharged!!! Uhmmm, EXCUSE ME! NOT POSSIBLE! I SHOWED HER MOTOROLA'S BOOK, SHOWING THIS. If these batteries could overcharge, we could not use the docks, now, could we???
She gave me a new one, and I have not had a problem since. I moderate at a forum for smartphones, and I have learned that there were a bunch of problems with the first batch of Droids. EXCHANGE IT, EXCHANGE IT, EXCHANGE IT!