Assign a static IP address to your N800 by editing the connection in Control Panel, and clicking the Advanced button on the last page of the configuration wizard.

Using an infinite lease time is a good way to ensure your DHCP server eventually runs out of IP addresses!

The best option would be to get to the bottom of this network issue and try to understand why your router began blocking your N800 - putting the N800 in the DMZ isn't an ideal solution, even with a static IP address.