I had this same problem and could not find an answer to save my life, but I think I have it. It wasn't WEP, distance, or anything. But when I logged into my router and changed the channel to 6 instead of 11 everything worked just dandy! (At least it hasn't kicked me off the internet again!) I hope this works, and if it does, please spread the word on another forum.
I have a Linksys 802.11b router and have tried 2 different wireless devices with my computer. My download speed is about equal to a 14k modem. The cable modem is hooked to the router and wired to one computer and is fast. The other computer is slow, slow, slow. If I can't speed it up I will make a hole in the wall and run a cable to the other computer.