pg_connect(): Cannot create new link

I have the same problem posted by James Ward (Date: Mon, 15 Sep 2003)

I migrated from (postgresql-7.3.2-3 and php-4.2.2-17) to
 (postgresql-7.3.4-2 and php-4.3.3-6).

When I connect to the Database via php, I get the following message:

Warning: pg_connect(): Cannot create new link. Too many open links (0).

I didn't change any configuration file: everything used to work.
It's the first connection to the database
(max connections should be 32 by default).

Is it a bug ? Any solution?
Is there a chance to bypass it?

Thanks a lot.
Mauro Folcarelli