Yeah - sounds to me like either the router is losing connection to the internet although it could still be at everything else is losing connection to the router.
When giving out IP addresses, the DHCP server in the router normally gives each client an ip address with a lease of at least 24 hours, saving each client (PC etc) from asking for another one constantly. Normally all the clients will use the router as the DNS server too.
When this happens - can all of the PCs / laptops still talk to each other? Does each operating system report a connection problem or can they just not access the internet? Can they still print?
If they can still print, then the problem is between the router and the outside world.
I've had issues with adsl filters appearing to wear out over time causing periodic connection drops, with the router unable to re-connect until restarted (someone told me that they replaced their's regularly because they got dirty - but thats another story
). Also with a tree rubbing against a phone line - although in this case the router just seemed to be constantly re-connecting (you could also hear the interference on the line...).
HTH