Is kazaa just diconnecting or is the cable modem disconnecting from your ISP?
You should not be getting disconnected from your ISP at all. The problem of getting disconnected might be due to an issue with your ISP and not the program.
Try running the computer without loading the suspect program, don't use the program for several hours, see if you get diconnected. If you do get disconnect, then it could be a problems with your ISP or the cable modem hardware. Contact your ISP.
If you don't get disconnected, try running the program again. If you once again get disconnected, maybe the program is causing a problem with your DHCP client, or it is trying to dial out with your dial-up adapter.
If the problem is unsolveable, don't use the program, find something else that works.