increse ulimit on your server.
Linux kernel by default limits to 1024 open file handles, open sockets / connections are also threaded as open file handle.
you can check how many are open and from where by typing
for how to change it see: http://wiki.alfresco.com/wiki/Too_many_open_files
default limit is really low, and for any server does anything remotly intestesting it should be incresed.