Hi,
I would start with checking CallManager and verify that you don't have any database issues (see link below). I would also check the phone status message to see if anything is getting logged prior to the issue.
CUCM Database Troubleshooting guide:
https://supportforums.cisco.com/docs/DOC-13672#comment-5297
How many CUCM nodes are in your cluster? You can also try changing the CUCM groups for some of the 7975 phones to see if the problem is more prevalent on one node or another.
If you see more phones acting up, I would recommend opening up a TAC case for more assistance.
Good Luck,
Brad