Now after your extra testing if it were me I would do those things that Sinitro suggests, then do the second battery that I suggested.

If it is not road vibration it could also be hotter conditions either inside the radio or in the car wiring. You could narrow this down by testing in the cool of the night or hottest part of the day, perhaps even run the car heater.

In radio repair at the circuit board level it is very common to either
heat (small nozzle on an adjustable heat gun)
or cool individual components ( freeze spray can)
to find annoying intermittent faults.

Some multimeters like the Fluke 87 have max/min recording so that you could connect such a meter to your 12 volt supply lines and see if the car wiring momentarily drops to a low level.

Good Luck.