I have a Rexing Dashcam that I've used for a couple years, and lately it's been behaving badly. It works perfectly fine while on, but when it's time for it to shut down, it often will shut off early, then reboot over and over until its internal battery is totally dead.
Everyone on the net says it's a bad card. Nope. It does mess up the card's partition by quitting in an uncontrolled fashion and by rebooting over and over, but I took the thing apart and the real problem was that the little internal battery is swollen and almost dead.
All the battery does is provide the camera with up to 30 seconds to save the currently captured video and perform a controlled shutdown, and as such, it's quite small. The battery in my V1LG was a 602040 3.7V 450mAh lipo. It was pretty badly swollen (they are supposed to be relatively flat). I've ordered a cheap replacement for $7, which is a lot cheaper than a new dashcam.
Anyway, if your dashcam is behaving oddly at power-down, and you've tried different cards with no success, it may be your battery.