Help - Public Interface seems to go to sleep

["David Culp" <dculp@xxxxxxxxxxxxxxxx>]

I have a dual-homed linux server  (RH 7.3).
     eth0  - private network
     eth1 - public network

     iptables/netfiler:
          Policy :  Deny All
          Eth0    : Accept All
          l0         : Accept All
          Eth1   :
               - Incoming:  Allow only TCP to port 443
               - Outgoing: Allow only established connections

     Problem:
          - Everything works 'most' of the time. However after no
            activity on the public interface for a while (hours), can not
connect.
            But then later, can connect ??
           From a tcpdump trace on eth1, the times that it will not connect
shows
           only SYN packets from the other host, no ACK from this server?

          Have I filtered out too much traffic ?  Should I allow ICMP through
the
          public interface ? Bad ethernet card ?

Thanks for your help,
David