Which model of Linksys is it?
My guess is you are running your router in Wireless mode correct?
My two suggestions are:
1. (a)
Tip: Purge the Downloads Queue! (click on blue link), so that the high number of incomplete files do not flood the router when LW is trying to connect.
(b) Set LW to only connect manually. Go to LW's menu bar, Tools -> Options -> Connection, & disable option to connect on startup. Then when starting up LW, wait 2-3 minutes. Then go to menu bar, File menu -> Connect.
2. Port forward the Linksys. I cannot give specific instructions without knowing the exact model number.

(connecting to your Linksys via ethernet cable would also increase reliability.)