I experienced many of the same symptoms you have been describing.
My climate control system failed intermittently. I knew it wasn't a loose wire--at least, symptomatically, it didn't appear to be.
I could be idling at a light and the AC would falter, go off for several seconds, then back on and run perfectly for the rest of the day. Other times, it would fail and stay off for the duration of the ride. No consistency.
Then it failed for good. No amount of coaxing, resting, praying was getting it to fire up again, even intermittently.
After reading this thread, I decided to pull the PC board for the climate control. Found a couple of suspicious capacitors; they'd leaked.
I took it to a local electronics guy (someone whom I'd given a ride in the NSX and who LOVED the experience). He said he'd try to fix it for me.
He replaced ALL 13 caps, noting he wasn't sure if the thing would work or not because some of the traces had been eaten away by the leaking caps. He rebuilt the traces as best he could. He also indicated he put higher-temperature-rated caps back in.
Reinstalled and voila!!! Ice cold air. The "FULL AUTO" works like a charm.
Paid the guy $75 for his time. The cheapest fix I've had on the car!
Jeff