OK, an update with new data....
Beginning in late fall the problem essentially went away. How convenient. Recently it has resurfaced. It seems to act up in warm weather.
I don't think it's the FSR. There are no symptoms to suggest that's it.
In the morning, when I first start the car the fan works fine, often throughout my 40 minute commute. Later in the day (lunch sometimes or usually on the commute home) it tends to work for about 10 minutes then quit. In the past it would cut out for only a few minutes (sometimes seconds) and come back on. Lately it has taken longer. Yesterday it did the usual work for 10 minutes and cut out. When I stopped for gas it started working again and worked fine the rest of the day. This morning it worked fine. On the way home, however, it got bitchy again. Worked for 10 minutes and cut out. I turned the IHKA off for about 10 minutes and turned it back on and it worked for 10 minutes and cut out again, this time for the duration of my trip, regardless of the little tricks I've employed in the past to restart it. I turned the AC off and on, varied the fan speed control (the IHKA shows the speed the fan should run). Nothing. When I turned off the AC I would get cool air drifting through the vents, but when I turned the AC back on, it would stop.
So, for sure the problem is one during warmer temps (it was 89F today so the commute sucked).
I suspect the IHKA could be bad, figuring when it heats up it cuts out and when it cools back down it works again.
The other suspect is the AC system itself. It could be perhaps low on refrigerant and the pressure switches are saying "no." Or it could be a bad expansion valve. I suspect the rest of the AC system less because it works fine otherwise. I may stop someplace tomorrow and have the 134a checked and topped up if necessary.
I have another IHKA from my 328i, but looking through Bentley's it appears the IHKA needs to be coded to the car and that is currently outside my toolset.
So, armed with this new data, do any of you have anything more than a WAG regarding what the culprit is?
Normally I'd just take it to a trusted shop and have them take a look at it, but I have a crazy-@$$ week with meetings ALL day tomorrow and court testimony Wednesday regarding the guy who ran into me last summer with a cement mixer. Then I have meetings all day on Thursday and Friday is the last day of the month, which means I'll be swamped. Saturday will be my first possible chance to have a shop check it out, but I'm running 17 miles in the morning and don't know when I can get to a shop. Like I said, crazy-@$$ week. And the following week I'm closing the books at work. So, any initial help I can get beyond a WAG will be greatly appreciated.