Thats strange, the only thing I can think of that rebooting the pc would do is either remove some cookies or allow the router to reset your IP address on your pc.
When you unplug the router and plug it back in can your other pc access that site or does that have to be rebooted too before it will access it ?
Unplugging the router would give you a different WAN IP address when it reconnected but it shouldnt alter your LAN IP addresses.
So rebooting the pc shouldnt really be necessary if theres something blocking your WAN IP from that site after so many connections for some reason :?
