Interesting - I haven't seen that one. But, unfortunately, database errors are inevitable from time to time. Sometimes the MySQL database server will become overwhelmed because too many processes are trying to access it (and not just from the forum, but from all of our host's Web sites that have access to it), so it kicks some of them out. Also, that error can occur whenever the server is briefly shut down for maintenance and such.
The good news, though, so far as the original subject of this topic goes is that we've changed hosts since I posted the warning, and I haven't seen the "Process limit exceeded..." error once since we've done that (whereas it seemed like it used to pop up at least once or twice a month). That may be due to the fact that we now have our own dedicated IP address. I know it has definitely helped the forum run the quickest it has ever run with any host.