Just found the problem for myself. I wanted to post on here to share the solution that worked for me.
It appears after years of having this phone, there seems to have developed a short circuit, or otherwise bad contact on the motherboard.
Regardless, I was able rather easily take apart the device following this video on youtube:
Then, I notice that if I lift the motherboard at the bottom of the phone (where the usb cable connects) the problem is solved.
So it appears the restarting in my case is solved by putting an insulator of some sort (some thin piece of plastic) between the bottom of the motherboard and the surface that holds the battery.