I leave Theatre View in that state all the time, and until recently I always allowed my HTPC to sleep, with the drives sleeping well before the rest of the PC. What you are seeing is a MC crash.
I suggest that you shut down the Media Server component of MC, which must be running as you see something in the system tray after the main program crash, and then turn on logging and leave MC Theatre View in a submenu that causes the problem, and wait for it to crash. Then look at the previous log included in the log zip file to see if there is any obvious reason for the crash.
I don't know of any way to selectively stop the SSD from sleeping, but I would be very surprised if the SSD sleep state was the root cause of the problem you are seeing. Unless, maybe, you are using MC Clients for each TV and the Client is calling on the MC Server when the SSD is asleep. But even then, unlikely. I can lock up the MC Server from my Client if I am doing lots of unusual testing or starting and stopping lots of media quickly, but I can't crash the MC Server doing that. It just locks up and stops responding.
BTW, do you have all connected TVs playing the same thing, and as you are using Infrared remote in each room, do you have an IR receiver in each room that is connected back to the server? Or do you have a MC Client such as a NUC or similar for each TV? Or are you using a DLNA Client on each TV to connect to the MC Server, and hence you are actually using the TV's DLNA interface to pull content from the server?