Mine stays plugged in so that the fridge stays cold and I have 120v there when I need it, except that I turn OFF the breaker on the 120v to 12v charger to the battery, and the battery is maintained through my solar panels, which do a much better job of topping-off and "floating", as necessary.
Plugged in full time while parked at home. Converter does a good job of maintaining the batteries whether full charge, topping off, maintaining, or desulfating. In the almost the 2 years I've had the MH I haven't had to add water and I check it often.
I unplug ours and disconnect the battery when we are not using it. It takes seconds to reconnect the battery and to run the cord to power when we are getting ready for a trip. Why waste the power and run up your electric bill.
Mine is plugged into a 20 amp receptacle when parked. I keep the battery hooked up year round. Being plugged in allows me to use anything I need in the RV anytime, except the A/C.
Mine stays plugged in 24/7 as well when I`m at home. My unit will be 7 yrs old in September and it still has the original group 24 Interstate battery so that is a testament to the battery tending capability of these new smart chargers.
I usually let mine sit for a week or two unplugged, then plug in for a week and let it charge/desulfate, etc. I have twin 6V with an upgraded smart charger that treats the batteries very well. I wouldn't hesitate to leave mine plugged in all the time if I had to. In the winter, the batteries come off the trailer and get maintained by a Battery Tender.
I remove the battery and take it home for 2 reasons. I have had propane tanks swapped ie a full one removed and an empty put in it's place... not imagining because they were different colors... And I use the battery for my winch that launches the large model gliders I fly. When not in use the battery is in the garage floor on a smart tender.
I leave mine plugged in at home. The fridge give me somewhere to store excess drinks bought in bulk.
My dealer / long time sales guy said keeping the fridge running would make it last longer. Don't know if that's true but like I said, I've got extra cold storage for things that don't need to be deep freezed.