so you need two out why there is a problem...
the message is simple enough there are more connections being requested then are available.
so the easy approach is to increase the number of connections. that can be done in either the PHP INI file and /or the MySQL ini/config file.
but that cures the symptoms, it doesn't necessarily cure the problem. you need to work out who / what is consuming the available connections, coudl you sue pconnect or soemthign simialr to share connections?
is it your application thats doing this or is there a rogue process from another app wanting to use the MySQL server? PHP will sutomtaiclly clear up after itself, other environments don't, nevertheless I'd argue its better to close a connection in PHP as soon as you have finished with it, releasing it for use by others.
it may be you need to permit more connections and increase the memory available on the server running MySQL.... each connection consumes resources and thats why most installation limit the number of connections to preserve throughput
I'd rather be riding on the Tiger 800 or the Norton