Hi Joey,
Sounds a little bit like the problem I had.. However, I did get an error message before the reboots. I have sent in the phone for warranty, and received a new one.
Try this, as indicated by FP support, for more diagnostics:
" 1. Open the Phone App
2. Dial *#*#66#*#* in the same way you are entering a phone number to make a phone call. Once the last character is introduced, the Service Menu appears showing you three sub-menus.
3. Select Service tests > Test Single
4. Press Battery status check . This test displays battery-related measuring values.
5. Take two screenshots : first when you are charging the device and then when you are not and send them to us.
If you want to stop the test, tap Back navigation key. Choose FAIL or PASS accordingly.
"