Do you really mean WEP? You should really be using WPA, as it is much more secure. WEP is outdated now and can be cracked in minutes.
You could try installing <a href="http://www.netstumbler.com/downloads/">Netstumbler</a>, which is a tool for diagnosing wifi issues. it could be that this router is using the same channel as your neighbour, for instance, and the two are affecting each other. Changing to a different channel might help.
Do the router's logs reveal anything? Is the disconnection happening at the same time of day, for example?

Do you get a decent wireless signal strength?
If you are you are using Windows, it will show the relative strengths of wireless access points near you.
Actually, I found that WPA was slightly more sensitive than WEP to weak wireless signals.