I'm not sure there is any real advantage to leaving it run. I wouldn't waste the electricity..! To me that's kind of like letting your toaster run in case you want a piece of toast for breakfast in a month or so.
If you forsee impromptu trips that come up spur-of-the-moment, it will be cold and ready to go whenever. Otherwise, plug it in the day before loading it up so it has a chance to cool off.
The main thing to keeping the frig "healthy" is NEVER run it when not relatively level. That includes a sloping parking lot when you park to go in and eat. (I level with the jacks when that happens) I even shut mine off when going up/down long steep hills. Mine has a 12v kill switch in the cockpit so all I have to do is switch it on/off at will. My main problem is remembering to turn it back "on".