Aging batteries can show a good charge or charging but will quickly deplete available amps under a load. Your convertor/charger probably does not have enough capacity to recharge AND move a large slide. If the engine alternator can be cross connected to the house DC circuits you might get by but either way after ten years you got a lot of life out of the batteries.
I'm running two Sam's Club 6VDC GC2 Duracell batteries in my coach. No problems after three camping seasons. Sam's gave me $15 core pay back on the dead 12VDC batteries which took the price down to just under $65 each. AGMs are nice and are worth considering but when you can get two venting batteries for less than the price of 1 AGM it's had to pass up.