strange connection problem

[Mike]

I have been running Fedora Core 2 for several months now,
and have no complaints, except for a weird connection problem.

It seems that whenever I try to connect to the internet or
another computer, it comes right back with host unavailable, or
connection refused, or no route to host. This happens for about a
minute, then I am able to connect fine after that. But if the
computer is idle for several minutes, I get the same thing. it doesn't
matter if I am using mozilla or just trying a ping from the shell.
I've searched archives, and all over the net, to no avail. This isn't
a dialup connection, and it is a permanent IP.

Anybody have similar problems? or point me in the right direction.
Thanks, Mike