Too many clients

I hope this goes to the right place!

I occasionally get the error "too many clients" when connecting to the
database. I try restarting the Postgres server and also Apache, but the
only thing that clears the problem is restarting Linux. I have maxusers
set to 35, and I am the only user, so I suspect I am not doing something
in my scripts that I should be, or doing something that I shouldn't be!
I have the pg_connect at the top of the script so each time it loads the
page it does a new connect - maybe this is a problem?

Probably a simple solution, anyone know?
Thanks
Andy