[JRTJH]

Something to consider if you store your trailer in a "community lot" or "commercial storage center": Storing it with the leveling system feet down, then removing the battery will prevent anyone from being able to move your trailer in the event of an emergency. This may be "good" if you're concerned about theft, but in the event of a fire, having to move trailers to prevent damage, or other reasons, if you put the jacks down and remove the batteries, you might prevent your trailer from being "saved" in the event of an emergency.

If you store on your own property, the same applies, but maybe it would be easier to "throw a battery in the trailer and pull up the jacks"... then, maybe it wouldn't. YMMV