My desktop is hard wired to cable isp and laptop by wireless to a Linksys router.  Recently the connection has been cutting out. In order to restore the connection , I must reboot. (Note: When shutting down, the computer pauses in the shutting done mode and I must manually shutdown. Also, the desktop computer has no connection problems.)  This problem is random and the connection dropdown menu just says connection failed.  Can this be a hardware problem or software?

Have you tried unplugging the router and then plugging it back in again?  I have to do that with my D-Link router at least once a day.

I had the same problem and did what Ray said, i.e. unplugging the router and plugging it back in at least once a day.  But then I heard some folks at work suggest changing the channel setting in the wireless settings on the router.  So I did that and it seemed to make a pretty big difference.  Now my wireless connection gets dropped maybe once a week if even that much.