Drivers won't help - they are for helping the 11R communicate with your computer. Startup is something different. I think the 11R has some marginal clock timing issues: it is a hardware issue. Just do a search and see how many people (including me) have had this intermittent issue on different forums. Mine goes into a coma if I switch the clock rate from either the front panel or the PC after it is warmed up a bit. Then it won't restart properly until it has cooled off. Others, like you, just have a bad day and they seem to not restart properly...
It is possible that it could be a loose connector, and that is worth checking out, but it is probably something else.
I would say if you get a quote for over $250 I would just buy a new or used unit on eBay without protools.
Sorry you are having so many issues!