Laugh if you want but we started seeing this when Vista shipped. The new BROADCAST FLAG which MSFT turned on created not only connect issues but the effect you are asking about.
USUALLY the latest router firmware cures this.
Yesterday my father brought home a Lenovo G450 running Windows 7 from work to replace his old relic of a laptop. The problem is that whenever I attempt to connect his laptop to our wireless router (a Linksys WRT54GS) the router begins to restart itself every 15-30 seconds kicking everyone off the network until even my own computer doesn't even bother to reconnect.
I should mention that I have two other laptops besides my main desktop computer (which is connected via ethernet cable) that are connected to the network, a macbook pro and a dell inspiron, and in the three years I've had this Linksys I've never once had a problem like this (or any problem for that matter).The Lenovo itself will show that it is connected to the router but it doesn't hold the connection due to the router rebooting. When I disconnect the Lenovo from the router the Linksys doesn't try to reboot and the other computers on the network have an excellent signal.
I've also found that removing the security from the router entirely fixes the issue, allowing the Lenovo to connect just fine with the router not trying to reboot, but this isn't ideal for obvious reasons. I was using a WPA Personal security mode with a TKIP algorithm before we got the Lenovo which is obviously causing some problems between the two, but I haven't bothered with any other settings yet to confirm it's the security settings.
My inquiries on the internet came across a suggestion (not directly given to me) to update the firmware on the router, but as luck would have it I'm running a Linksy WRT54GS v7 which apparently isn't supported by Linksys...so I'm not sure what options I have left.
I'm willing to provide any additional information in the hopes that someone can find the problem.