I had similar problem earlier.. first error from came from max sessions, then i kill'd session from buddyauth, and restarted db, then came "db has stopped working" .. that was the cycle. I ended up deteling whole db folder and re-installed it, that one helped...
this whole problem came exact after installing relogger, dunno if there's some sort of relations between these apps thou...
I just signed up for the 3 day trial as well and had the same issue;
I would start Diablo 3 -> Login -> open DB and enter key login, it would flash my D3 windowed screen and a few seconds later DB would get windows popup that it had stop responding (I would close) then if I attempted to restart DB it would give the Max Connection issue. Log out log back in and same issue.
Latexii post about relogger helped, I had download YAR and I placed it in the extracted folder in the DB\Plugins folder (I'm new I guess I shouldn't of done that). I have since moved it out of that folder and restarted and everything is fine now.






