Linksys user manual will show how to secure using WPA key for instance, which also needs to be entered in Windows on the network setup screen.
Help screens should tell how to set this up. Or read the user manual - try to find the one you need here (or maybe they have it on CD that came with the router)http://www.linksysbycisco.com/US/en/support
As far as dropping the connection - one thing is to tell the router to keep alive always which means don't drop the connection with ISP if computer is idle. Also don't allow Windows power features to shutdown your NIC. How? Computer user guide might tell you.
Additionally, if you use a firewall, you should permit DNS servers and DHCP server to be permitted entries rather than blocked or untrusted. The rebooting you have to do simply forces Windows to start the connection with the DHCP server, but Windows can only do it once, when it boots. Then it's up to you to maintain the connection.
Also see thesehttp://support.microsoft.com/default.aspx?...kb;en-us;314067http://support.microsoft.com/default.aspx?...kb;en-us;308007http://www.microsoft.com/windowsxp/using/n...oubleshoot.mspx