hi
it has nothing to do with your linksys wlan router
I assume your pc or laptop goes into powersaving mode. when it comes back into normal mode, you lost your connection to the wlanrouter. actually not the connection, the authentification is gone. same happens when you work on your laptop / pc and you switch the router off and on by accident :-) . then you have the same effect. both are up and running but not connecting. I have the same effect with two laptops ( same brand) , but one of them gets the auth back the other has to be restarted to work properly again.
so switch of the powersaving mode !