I've had many a battery still giving you a good Volt reading, but as Joker said........a bad cell and they will die as soon as any load is placed on them.
Your overcharging problem can FRY a battery as well.
They DO NOT like heat, and overcharging batteries give off enough to cook your dinner with!
Fix your wiring, but make sure you top it off with a good new battery as well.
Good Luck !