Could be a raft of things Don. dirty connections, weak alternator, the battery switch itself. Can probably rule out the batteries themselves for now since you did have them tested, but do you know how old they are?
While you were out do you know if there were any other loads operating aside from the radio?
If it is a simple battery switch when on "Both" the engine should charge both. Mine does, but it's tough to tell without looking at how they are wired.
Troubleshooting if you have a multi-meter: with the battery charger off check the voltages of both. Charger on, check both. charger off, engine on, chech 1st on position 1, then the other in position 2, then both in position Both.