Depends on what OS your running. PC based try this..
Check physical connections, make sure you have everything inserted correctly. Are you running through a router / hub ? If so try going directly from modem to your computer.
Start -> Run -> type cmd (If cmd doesn't work, your on an older version of windows so type command)
Type:
ipconfig /flushdns
ipconfig /release "Local Area Connection" <- Where Local area connection is, type the name of your connection. generally on cable it's going to be named that. If not find out under network connections.
ipconfig /renew
Check your TCP/IP settings ensure nothing has been hard coded here unless you have static IP's. If you don't have TCP/IP settings you'll need to add them (Since your able to connect for a period of time then you should have them)
Try running a netstat see how many active connections you have running to your computer, you may have to many things (Spyware, Ad-ware, Trojans, Viruses etc..) connected to your PC making your system hang and disconnect you.
If you are running through a router go to any browser and type 192.168.1.1 If you bought a linksys router UN - admin PW - (nothing) unless you've changed this. Other routers, refer to your manual or contact your vendor. (For example... Belkin, D-Link, Netopia etc) I'm sure they can provide you with something that will work. Once your here try pinging yahoo, see if all packets are received. Try a traceroute to the same site, see if there is a spot you hang on that may be causing your problem. Check your DHCP server here and verify nothing is hard coded (Again unless you have statics)
Uhhh.. Other then that.. Couldn't tell you really how to fix it, just how to find the problem. I do tech support for DSL not cable, and those are all things to try. If you find out the problem it's always best to give your provider a ring. Hope this helps finding your problem and learning how to go about your solution.
Edit: On DSL we have access to test, and whats called a DSLAM to see if the problem lies there. Since i don't do tech for cable they should have access like this, most likely called something else. And get your complaint in as early in your troubles as you can. Remember you can always ask for a pro-rated refund for the time your service was messed up. After all why should you pay when something doesn't work the way the provider guaruntees it.