I've a LINKSYS WRT54G as well, & have only had to power it down/up once due to connection problems with it in the past 2 years! Btw is it actually called a LYNXSYS in the states?
Routers do have memory & so can be prone to similar kinds of memory problems as PC's, hence the need to power down & up. I have a friend who's old router used to overheat as well & so needed some off time. Might be worth checking if there is more up to date firmware (downloadable operating software) for the router Sticks. If you tell me the make & model (via PM) I don't mind checking for you.
(I hope everyone's using WPA encryption now that WEP is now well & truely cracked btw).