It sounds to me like the caps are not retaining their charge well enough, plus that your battery voltage is so low at cranking that the cam(s) are shutting down from low voltage. The caps loss may be due to wear and tear, excessive time between charges, or both. The battery voltage may be a number of issues, bet here's the scenario: when turning the key to "on" (even momentarily as happens when you pass that position going to "start") that signals the cams to boot up. When the cam discovers a voltage drop below it's minimum, that signals the cam(s) to shut down or ut disrupts the boot process resulting in improper operation. It also appears here that one of your PS's isn't providing 5V to the cam well enough, probably because of the low car battery voltage situation.
If you've got an analog voltmeter you can measure the voltage at cranking on the USB side of the PS's to see if they are momentarily dropping out. A digital meter won't stabilize a reading quickly enough to show this 😉
I'm thinking you've either got a car battery on it's way out or it's not holding a charge well enough (too long between car uses or perhaps parasitic drain) to keep the PS's going during cranking.
Phil