We set up Win98SE 600 mhz machine (the slowest machine we have in our test fleet) and have been running it since Friday with 2.5 second ping interval, with 5 LAN targets and 1 internet target.
It's still running, with seemingly no problems.
We don't have any of the other utilities installed (RealVNC, AVG Anti Virus, Tiny Personal Firewall), so we're not running the exact same software as you. We're planning to let it run 7 days just to make sure we can't reproduce without any additional software, and then we'll add some of those tools to the game.
I'm not sure if you have a hardware firewall to protect that machine, but if so you might try uninstalling some of those utilities to see if it makes a difference. Just because the problem is TCP/IP related, you might start with the firewall.
Let us know your success on continuing efforts here, and we'll do the same.