I received a new mainboard for my trainer from Elite. The board came with factory‑installed firmware version 37.
In the past few days I have had 4 rides of 45 to 60 minutes each, 3 on the computer and one via phone. On two rides on the computer I had in a total two small connection losses of about 10-15 seconds each. So overall the problem is solved, maybe some additional minor firmware tweaking will be needed.