sometimes routers "hang" a connection - the router thinks its live, even though its not, but because the router thinks the connection is still live, it won't allow another connection from that MAC address. Rebooting the router should clear that - you shouldn't need to reset it.
However what I have seen happen a couple of times is where the router runs out of IP addresses to serve by DHCP. I've only seen this in busy locations like pubs and B&Bs where a lot of different machines connect transiently. If it happens its a fault of the router (the addresses should release, but don't) and on those occasions I've had to reset the router to get access back.
It takes a lot to push a router that far - depends on how its set up, but most have the full .255 IP range - so 253 connections