The real answer is that IT DEPENDS.
IF (yes, big IF) you have a smart charger, or smart inverter/charger AND it has been properly programmed for your battery chemistry, bank size and ambient temperature (or has battery temperature probe)leave it plugged in 24/7/365.
Earlier, "dumb" converters charge at too high a voltage for float. So, if this is what you have, it will harm the batteries to have then continually being overcharged. Best alternative: Buy a HD 20 amp timer from any box store. Plug the converter into it and set it to run an hour a day.