I don't think that would normally be possible, as nearly every rechargeable device should have some control circuitry which prevents over-charging/over-discharging. There are even "docks" which keep controllers charged like this all the time.
What could have happened is that your controllers were charged, then discharged very slowly, then charged again (over and over again) - over a very long time this number of cycles could impact the battery life. I wouldn't have thought a few months would be enough to do this though.
As all 4 have had this happen, it doesn't look good - have you tried unplugging them and charging them again to see what happens?
Leaving the console on the dock or plugged in directly with the AC adapter overnight, or past the point where the battery is fully charged will not cause harm to the battery.
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