Chip, one additional thought.....

If none of the above shed light on this then I suspect that you may be the victim of ARP poisoning (look it up). I would reset the router and test everything again with wireless turned off. I would also change the security key, and if using WEP be sure to use the longer 128 bit version, manually change the key frequently (daily is not unreasonable), and keep the wireless feature enabled only when you actually use it.

It will likely help if you give us more information on what you see when this IP assignment problem happens, that is, how does your network react?

As a last ditch "fix", and one that I would hate to resort to, you could set static IP addresses in the windows boxes that were outside of the dynamic IP range. That is, tell the router to hand out addresses between 192.168.0.100 and 192,168.0.200 and then set static addresses like 192.168.0.50 and 192.168.0.51 in the windows boxes. But there should really be no need for this and I would try to resolve the router problem, oherwise it will likely come back and impact you some other way.