Well. It would help quite a bit if you told me what type of internet connection you have. If you have dial-up, you could be experiencing the "rehandshaking" process when your modem searches for an acceptable speed after encountering numerous errors. If you have dial-up refer to your modem's instructions for information on how to slow down the maximum rate of the modem.
If you have broadband there are a few types of problems you may be having.
1. The line is loosing the connection. This is evident if the connection stops working randomly and then randomly starts working later. If you have DSL and this happens when someone uses the phone it may indicate that a DSL filter is not working or that one is missing somewhere in the building. Check your security system and / or fire alarm, these can cause problems with the DSL. If you have a cable modem try your connection with the modem connected right to the line coming into the building; eliminate any splitters or amplifiers as well.
2. If you are using WiFi try the connection with the computer plugged in with an ethernet cable. Sometimes, even with a strong signal, WiFi can cut out especially if there is interference from other cordless devices or other networks.
3. Traffic on your network may be causing you to loose the connection. If you are in a college dorm or on a business network you may not have any say in this. If you are at home try unplugging all the other computers.
Finally, it is possible that you do not have a fast enough connection (or one with a low enough latency) to do what you want to do. Satelite internet, dial-up, and GPRS (internet delivered through the cell phone system) often can not handle applications requiring realtime access to the internet such as streaming live video or games.
You can also go on www.speedtest.net and get some real data on your internet connection. Not only will it tell you your average speed it also includes a tool called ping test which tells you if you are loosing any data and how long each roundtrip communication is.
Best of Luck