System closing connections

All,
I am having a problem with my 7.2 servers.  I have a web application
configured to use box 1 as the "middle tier" and box 2 as the
database/application tier.  I am using PostgreSQL 7.3.2 as my database. 
However, my server is constantly losing the connection to the database. 
What's more is that also closes all other connections as well, namely
secure shell.  

The only consistent way that I have been able to fix the problem is log
into box 2 (at the machine as it accepts nothing remotely) and ping the
box 1.  After about 10 replies from box 1 it seems to clear up and then
I can re-open connections.  Then I have to repeat when it happens again.
It is starting to happen EXTREMELY frequently -- about every 5 - 15
minutes.  

A little information....
I am using Red Hat 7.2 fully updated with Red Hat errata.  I have
completely disabled my firewall as I feared that might be the problem.
I am using entries in my my /etc/hosts file to resolve the server ips 
and the DNS for the domain is handled on a separate box.

Does anyone have any ideas or has anyone seen this before?  

Thanks in advanace.

Regards,
Andrew Wellman

-- 
Andrew "AJ" Wellman
IT Manager
Support Services, Inc.
(720)489-1630