call an exocist...lol ( just kidding)
What I can tell from your post is that the heater/AC unit should be on it's own dedicated circuit, unless it is one of those window units and even then many recommend they be on separate circuits.
Have you checked to see that someone hasn't added a circuit from the microwave circuit, I've seen this happen so many times?
If the microwave is a counter top model, have you tried it in a different outlet (don't use it, just monitor the clock function during the day) and see if the losing time still happens. Or if possible and it's an over the range model try using and extension lead into a different outlet ( again "don't" use it for any purpose other than checking the clock function through out the day)