Is it better to leave a battery connected to the charger, or to charge it only once every few months?

You can basically just leave a battery connected to the battery charger, provided it is a so-called trickle charger.
A trickle charger is an intelligent battery charger that provides the battery with just enough current to stay fully charged without damaging the battery. Battery chargers without a trickle charge mode can potentially damage the battery by “overcharging” it.
So if you use an intelligent battery charger that automatically switches to trickle charging, you can leave the battery connected to the charger without any problems. Read more about how to charge a battery here.

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