I have a similar issue with the asi585mc pro in combination with the latest asiair plus. I'm on 2.3 11.56 software.
After shooting 2 or 3 frames in autorun mode it would briefly stop the cooler, then it would start again, but would overshoot the target temp (-10C) and keep cooling. It got to -21 and sometimes at 99% power use.
I'm testing now with a separate power supply as I have also exactly the same experience: connecting everything with my laptop and Asistudio or Nina had no issues whatsoever shooting these darks.
Here I was shooting the first frames 
And then suddenly it stops the cooler and the autorun seems to hang also.
No more counter for amount of exposures, no more counter for time.
In Live mode the setup worked fine previously, but I want to take more darks than 20 and work with my own darks library.
Edit: after running into the issue and trying the 2 minute exposures for darks in live mode it also doesn't work. 
I got an exposure failed message.
