This error suddenly showed up about 3 days ago and it has steadily gotten worse to the point that our log files are now filled with this error and the site is effectively dysfunctional.

I am seeing the following show up in the PHP logs:
Code:
mysql_connect() [function.mysql-connect]: Can't create a new thread (errno 12); if you are not out of available m
Any idea what could be causing it and how I could fix it? This never happened when we had 1 GB of RAM installed but now it is suddenly happening after doubling the RAM to 2 GB about a week after adding that new RAM.