Before you start messing w/ rebooting (and facing a possible long drive) I'd suggest you login to that machine somehow, and perform some basic packet analysis (tcpdump,ethereral) to see exactly what is happening. If you don't see anything there, check the gateway machine (or whatever connects your C network to the B/A networks.
Not having any clue as to what that machine is doing, you may have to fine tune this command to filter out other traffic:
SSH to the problem machine, then type
tcpdump -n not port 22
Assuming it has a single interface, that should show all the traffic entering and exiting that machine, excluding yours (and that of anyone else) SSH traffic (from the login you're doing).
Try pinging from one of the outside systems, and see what's happening....
I suppose that if you don't see anything weird, you might also consider the machine has been compromised somehow and it's current environment is causing the strange behavior. FWIW, if the machine has been hacked, you shouldn't really trust what tcpdump is telling you
Jon
