Problem solved 
I checked virtually every connection. I cleaned the entire inside of the laser. I added additional ventilation. I tested two other good quality USB cables.
None of the above helped — the laser was still stopping randomly.
In a moment of desperation, I remembered an absurdly expensive USB cable that I use for data transfer from my camera.
Using that cable solved all the problems.
Most likely some kind of interference was occurring and causing signal issues. This is only an assumption, as I’m not an expert, but logically it’s the only explanation. The camera USB cable has much thicker insulation.
I hope my problems and stress are finally over. Maybe this description will also help someone in the future who runs into the same issue.
Thank you for your interest