Nothing to do with the WI-FI coverage!

What that means is (You have either Vista or 7 btw, more likely 7 I should think) it means what it says, i.e. your PC can't see the outside world, i.e. the internet and only the LAN, when working this should say "Local and Internet"

In other words, your router is loosing it's connection to your ISP and by resetting you are resolving this issue, it maybe your provider only has a short "DHCP lease", hence after x number of days or hours it drops the connection.

Martin