i am rooted, but i found a fix for me.
yes, my phone would turn off and then on, doing a reboot, reloading the screen icons and scanning the sd card at least 5 times a day even if i was not using it.
i had turned off/unchecked "auto sync" under general sync settings. this turned of/unchecked auto sync for contacts, calendar, gmail (i deleted google books) to save data usage. to keep contacts and calendar up to date, i would do it myself every few days manually thinking i was smart. i do not use gmail on my phone.
under settings, go to accounts and sync, then see if auto sync is checked on. i had experimented by only turning off auto sync, but leaving gmail, contacts and casendar turned off. by turning on/checking auto sync and ALSO calendar, contacts and gmail, i got it to stop.
i repeat: i experimented with this, and this was the only thing i changed and then it stopped. i had uncheked auto sync. i fixed it by checking/turning auto sync back on, and making sure i also went to the next page and checked/turned on gmail, calendar and contacts.
it is possible to only turn on auto sync, but to turn off calendar, contacts and gmail. i believe this was the cause of it rebooting for me.
after i did this, it stopped rebooting 3 or more times per day. for some reason, the phone got mad when auto sync was turned off, and even if auto sync is turned on, you need to go to the next page and check/turn on gmail, contacts and calendar.
at least try this, it worked for me, and when i turned the above settings off, it would reboot 3 times a day for no reason. apparently, turning off auto sync, AND turning off contacts, gmail, calendar makes the phone mad.
let us know if this fixes it!
if you have never turned off auto sync, i do not have a solution for you, sorry.
good luck..