RoyB — this is a television, not a (car) radio, though the concept is similar. I doubt the television has a separate memory power lead, though.
If the television is AC powered (rather than DC powered), you may be out of luck unless you put in an inverter just to keep the channel memory active. If it has a separate power supply brick, check the output voltage of the power supply; many are 12V and in that case you can just wire the television directly to the camper's 12V system and get rid of the power brick altogether.
If it has a battery back up for the clock etc., make sure the battery is fresh. I don't think many televisions have such a back up, although the little under counter one mounted in my motorhome by the previous owner does so at least a few do.