On XP, OS X and Linux a freeze of internet connection is mostly due to a poor hardwares: network card if the problem is on the computer, modem or router on the network side. You might want to seek for updates firmwares for those equipment if you can. If nothing does, and you really want to do P2Ping which is network hardware intensive, change the modem or router, that's about it.
On OS 9 users might also want to increase the memory allowed to LW to 80mb (ctl-i on the LW application icon).
Bonne chance