Internal network OK but can't ping router?

I have the following network:

WinNT4 Metaframe Server
DAVMFRAME
192.168.1.5
|
|
v
192.168.1.18
Cisco 770 router
10.0.0.1
|
|
v
10.0.0.2
Cisco 770 Router
172.16.8.1
|
|
v
WinNT4 Domain Server
WAREHOUSESERVER
172.16.8.4
|
|
v
Network of computers
Running Win9x, WinNT4 WS, WinXP
DHCP clients

The problem I'm having is that if a workstation (on the 172.16.8.x network) is switched off at night, when it is switched on in the morning, it can access the whole network EXCEPT the router. I can ping all other PCs on the same network from a Command prompt but not the router.

IPCONFIG shows a DHCP-induced IP address, subnet & gateway for the problem workstation (the gateway IS the router).

It is a random occurance. The only way to fix the problem is to turn on all workstations, then power-cycle the router. All workstations can now ping the router.

Why is this happening and how can I fix it?