Unfortunately then it seems like your best course of action is to perform a full IOS restore using iTunes. Make sure you make a backup first using either iCloud or iTunes depending on how you have things set up. You can then choose to restore the backup once IOS has been reinstalled if you like.
If the device still behaves this way after a full restore then it points towards a hardware issue.
If you happen to still be under warranty, a trip to any Apple store would likely see them replace it for you on the spot. Best to take it in when "frozen" so they can see the issue for themselves, and explain it reoccurs after a reset consistently. If you do take it in, they will likely insist that you have tried to fix it by restoring it, so best to try that first.