That come and go so quickly makes it hard to sort but then a few questions may start in the right direction?
For the sorting, we need to get into whther it is a 110AC or a 12VDC problem---or both!
Maybe you know this but the frig may be either, so do you know for sure if it uses only 110 or only 12VDC?
Then the vent fan, that would seem to be only 12VDc working off the converter and batteries.
The TV is normally 110 but may be working thorough an inverter, so when it stops, looking at whether you are plugged or using inverter can be a clue. As you mention boondocking as no prtoblem, I would assume the problem with it would be the 110AC side.
Can we assume it has happens enough that you are sure it is not just a local or campground outage? Reason that comes to mind is that we are in a fast growing area here in Central Texas and electrical outages are common. It goes out for 10-20 minutes to an hour and possibly twice a month!
A little more thinking about when and what may be needed as first thought is a 110 AC problem but that would not be expected to fail the vent fan running on batteries at 12VDC, so something to check.
If it is only an AC problem and it can be ruled out as a campground or local problem that effects a number of others, I would look carefully at several of the small points on the RV.
Starting at the plug to shore power, is there any sign of arcing on the plug? If the plug is worn or hanging so that it tends to work loose in wind gusts, etc. there should be obvious signs of burning on the blades of the plug as it will arc as it loses and regains contact.
Next might be to leave the cord plugged and then wiggle the cord near the plug as a way to look for conductors nearly broken inside the insulation. Looking for something that may lose contact with a slight movement?
Same might be true at the point where the cord enters or connects at the RV. I see you have an automatic transfer switch. That "might" be a point to check for arcing but I lean away from that being a true cause that would repeat to disconnect and then reconnect. I tend to think of them as wires that get loose and die pretty quick due to arcing and long term until fixed!
But it might be worthwhile to take a look inside the box for luck and while there, tighten these screws as they do seem to be a semi common failure after some time. any smoked parts?
Be sure to disconnect from power first!!
This is more of a group of suggestions as come and go is often just finding a cause by organised luck as much as anything!
The question of whether the 12Volt is also failing can really throw it into a whole different area! A true 12Volt failure would seem likely to happen on boondocking as well, so things may be tricking you!
Good luck on finding something as you do seem to have a bad one to sort!