Internet Connection Sharing - DNS Proxy stops serving if user logs off host

I have cause to use a Windows XP box to connect my laptop
to the Internet at times, and I have noticed that, if the
person using the host logs off, the DNS proxy stops serving
my client computer (which is normally running Linux).

I can see two possible cures, but no way to achieve either
of them:

(i) set the host so that the DNS proxy continues to serve
ICS clients after logging off.

(ii) set the host so that it provides the addresses of the
real DNS servers by DHCP. The machine always uses DHCP or
BOOTP anyway due to the diversity of networks to which it
is connected, and I have configured my home network DHCP
server to put the desired address on it.

There is no mileage in setting the DNS server addresses
manually, as it would then need to be done every time the
client is connected in this way.

I will return here for responses, but sending them by email
if you can would also be helpful.