I thought CopyMan was one of my colleagues as we are in the exact same issue. We have about 12 8703e's that spontaneously reboot - mine was rebooting about 4 or 5 times a day, sometimes taking 45 minutes to reboot. We've upgraded the firmware, ensured no third party apps are installed (including google!) and still get the issues. Reboots also occur in the holster too.
Most of the time we get a "verifying security settings" message after the phone reboots but not every time. We've even had synchronised reboots where ALL the phones have suddenly rebooted themselves.
Eventually my device was upgraded to the 8830 and the reboots have stopped.
We're currently (as I type) talking to Sprint AND RIM to try and get an answer - paying for an "upgrade" to 8830's should not really be an option as the phones are not fit for the purpose if they don't stay online for 8 hours.

Update: After 45 minutes on hold whilst the Sprint rep spoke to RIM , we find that RIM do know about this problem and are working on a solution but no eta yet. If you would like to be informed of updates to the software by RIM then send an email to . subject line Email Update Request for Reboot Issue and in the body, put the fact you have an 8703 with issues rebooting at random and that you want email updates on when the problem will be resolved.