This problem just started for me 2 days ago.
I bought the phone on release date, and it is hardware version 002. It has been find up until I needed to actually use it on a trip. I flew from California to Orlando, and as soon as I got off the plane, and turned on the phone, the reboot problem started happening.
I can leave it on all night on the nightstand and it doesn't happen, but as soon as I try to interact with the phone, I start having trouble. I have noticed that it seems to happen more often when I have the GPS on, but it isn't necessary. I had the problem today, just sitting on the couch browsing the web with BT and GPS off.
I'm wondering if it is somehow related to signal string as I'm in a rural area with splotchy coverage.
I called Sprint, and they told me I have to go into a store.
I bought the phone at Best Buy and got their Black Tie protection plan, but I haven't tried to go in yet. I haven't heard good things about their protection plan, though.
I'm on Rooted Froyo using the Clockwork Mod recovery. I've tried restoring backups from late september, removing Flash Player, replacing the battery, replacing the SD Card, but nothing has worked. The only think that seems to help is to place the phone in the freezer for a few minutes. I don't know if putting it in the freezer is what is helping, or if it is because at that point, I have left the battery out for more than a minute and some kind of reset has happened.