Should I turn off the inverter...

[borderman]

...when connected to shore power? Residential refrigerator.

[Tbos]

When I’m home I turn it off but you don’t have to.

[tech740]

I don’t. If you loose power then you have no backup if you are away from the camper.

[ChuckS]

The inverter auto bypasses 120 volt AC to fridge when it senses incoming shore power. However... even in standby it is drawing current from battery and converter so why not turn it off

[JRTJH]

All devices are designed with a "Mean Time To Failure" (MTTF) or a "Mean Time To Repair" (MTTR) as a part of the design criteria. The question with your inverter longevity would probably hinge around that design criteria.

If the MTTF is extremely long, chances are you'll sell or trade the trailer before the inverter fails (statistically) so it wouldn't matter whether you leave it on or turn it off. But, if the MTTF is short, you might want to consider turning it off to preserve the "hours before it fails" so you won't end up replacing it, maybe even frequently replacing it....

The question then becomes: What is the MTTF and where do I find it?
Answer: Contact the manufacturer or use their website to see if you can get any information on the MTTF/MTTR criteria for that device.

Yeah, I know, usually easier said than done.

[travelin texans]

I'm guessing the switch to turn it off/on also has a MTTF, just have to find all the MTTFs for the invertor system before you make your decision. LOL!
My point is the system is/was designed to bypass when connected to shore power, what if it does use a bit if power, you're connected, so my opinion let the system operate as it was designed & you'll have one less thing to fret over.
To me it's the same as manually shifting gears in your vehicle with automatic transmission.

[MarkEHansen]

I had a grandfather who would drive down the street with his windshield all fogged up. When I asked why he didn't use the de-fogger (fan), he said because it will cause wear and tear on the fan and will eventually go out and cost money to replace.

I agree with Danny. Use it as designed.