I think this is your problem. . .possibly overcharging the batteries. If you charge them too much you build up heat and pressure inside that can damage them. The conditions you describe (sitting for up to 3 weeks) should not require any charging or battery tender at all. Your batteries (any auto batteries) should be able to handle that in a car in good condition with no problem. If your battery can't sit that long and still start the car, you have a parasitic drain somewhere or a bad connection. I use a Walmart battery in my C4 and it sits up to three weeks with no problems whatsoever. It will sit (albeit disconnected) in my freezing cold garage all winter and start first thing in the Spring.
Most battery chargers do not automatically fully shut off, they simply go down to very low amperage as the battery nears full charge. . .but they still charge. . .and that can damage your battery. I know a bit about these things. . .I use to work for a battery charger company!