Electrical – Temporary (multi-hour) voltage drop that seems instigated by running an appliance

I have a 15 amp circuit that runs to the laundry room and has on it:

1. An indoor receptacle with a lamp plugged into it
2. An indoor receptacle with an exercise bike plugged into it
3. An indoor receptacle with a gas dryer and gas washer plugged into it
4. An outdoor receptacle that rarely has anything plugged into it
5. A motion sensor light on the exterior of the garage

This setup has worked without any issues since we've owned the house (~7 years) and the outdoor receptacle was installed off this circuit by a professional electrician about 5 years ago and is in a hefty outdoor box under an eave with appropriate caulking, etc.

A few weeks ago the washer cut out mid-way through a wash. Using a multi-meter I measured a severe voltage drop across the hot and neutral, which reported ~60v. The lamp would turn on but it was very dim. We ended up using an extension cord to reach an outlet on the other side of the garage, which is on a different circuit, and completed the laundry.

What is odd is that the next day the circuit that was reporting ~60v was now back to 120v. The laundry machine would run again and we did a load without issue. The lamp was back to full brightness. I checked all three indoor receptacles for any loose connections, but they all seemed good. Nevertheless, I replaced all three. I also checked the motion sensor light and the connections were tight, there was no moisture or other issues with the junction box the light was installed on, etc. (I did not replace the light, but reconnected everything and put it back the way it was.)

The next weekend when we did another load of laundry the same problem happened: midway through the wash the washer cut out. This time the voltage reported ~40v, for whatever that's worth. Again, we used the extension cord and did several loads of laundry. I checked the circuit a few more times throughout the day and the same problem persisted – ~40v reported from hot to neutral and a dim lamp. The next day, however, the circuit was back to reporting 120v across the hot and neutral, the lamp shone brightly, the washing machine would turn on with the previously faulty outlet.

What is going on here? My questions:

1. It seems that the voltage drop happens only when using the washer, but it doesn't happen right when the wash starts, but midway through the cycle. But if it was the washer that was causing the problems, why does it work on another circuit?
2. Why does the voltage drop happen and persist for several hours and then miraculously resolve itself? I would expect that if the drop was due to a load on the circuit that once the load was disconnected or off the voltage drop would repair itself. If the drop was due to a loose connection or faulty wiring then the issue wouldn't resolve itself until that loose connection or faulty wiring was addressed.
3. Is there anything else I can try before calling a professional electrician? (I'm not comfortable mucking around at the service panel. Also, I'm too old / not interested in crawling up in the attic. I'd rather pay someone to do that, lol.) And what is the electrician going to be looking for? I worry this is going to be a very expensive repair since I (perhaps incorrectly) presume they're going to need to spend significant time trying to track down what, exactly, is the issue.

Thanks