I agree that the microwave clock resetting is indicative of a brief power interruption. The question is where. As was mentioned above, start with your shore power cord. Check for straight, clean prongs on the plug. Look for any discoloration on any of the prongs or the plastic around them. Do the same with the other end, where it connects to the trailer. Check for any discoloration on the trailer side. By discoloration I don't mean simple oxidation, but evidence of overheating.
Once the outside is done, go inside. Pull the cover off of the 120 V breaker panel and check all of the connections to be sure they are tight. Obviously, this step requires that shore power and inverter are off. Since the microwave probably has a separate breaker, pull it out and make sure that the connection there is also tight.
Now for the fun part. You get to find the outlet for the microwave and pull it out so you can look at it. If you are lucky, it is out in the open. It may well be somewhat hidden by decorative stuff, or even inside a cupboard. The good news is that Grand Design didn't skimp on the length of the wire, so there ought to be plenty to come out to change the outlet.
You may want to do all of this over a period of several days, so that if the problem is at the shore power cord, for example, you don't spend time going through all of the rest of that circuit. I'd still do it, though, just because connections do loosen up over time.