Yeah we ran into a similar issue with dreamhost. They oversell, and we had a busy weekend once and they sent us a similar email about too many connections. While we had many connections, no where near to many for the plans they sell. Went to a new host and no more issues.
I use dreamhost for personal sites, but anything important go dedicated, we use
http://www.rackspace.com you will need to have someone who knows what they are doing though.