I'm losing my internet connection everytime I put my system to sleep and have to restart to get it going again. I've got G4 tower, and running 10.2.8 with a cable modem.
1) Your ISP may require a constant ping (or routing of data) to stay up. But I believe this is probably not true in your case.
2) You have to ask yourself when did this start. Did it start after an update (10.2.8 or something else)?
If you just did, then try the 10.2.8 Combo Update. Believe it when I say the combo updates in 10.2.x are way better than the OS 10.2.x updates through Software Update. The combo updates replace system files insted of just updating them. The combo update will not hurt any of your installed programs.
3) Plus, always remember Mac OS X is BSD Unix based and every unix user knows unix LOVES file permissions. So, open Applications->Utilities->Disk Utility and Repair Permisssions after most every major software install. This will prevent a host of future problems in OS X after software installs.