pg_connect(): ...Too many open links (0)

Hi all,
I've searched high and low on the web and the group for the following error:

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

I have checked phpinfo and it says max_links is unlimited, and so is
max_persistent.

It's got to be something obvious - but I can't see it.

How can I have too many links open if this is the first one!?!

I'm running postgres 7.3.4 and php 4.3.3.

I can access the database using pgAdmin - so I don't think it isn't a
permissions problem.  I've got tcp/ip access enabled.

All help appreciated,
James