I wasn't sure if I should put this under i4 or iOS5. I bought an i4 yesterday, and updated it to iOS5 last night.
Since then it goes through periods of randomly rebooting or shutting off. Sometimes it happens while I'm in the middle of doing something (ie looking at settings, using Safari, using Music, etc), or in the middle of syncing the phone, or when the phone is just sitting on the desk.
Sometimes the phone restarts. Sometimes it just shuts down. If I press the start button on top, it will start again.
At work today I watched it restart 5 times in a 20 minute period. Right now, for the last 15 minutes it's doing the same thing.
Another thing that I've noticed is that after it restarts, the battery level will have changed by a few percentage points. Sometimes up, sometimes down.
Any thoughts on where I start troubleshooting? I'd be grateful for any comments.