DHCP-Enabled Router Sometimes Won't Talk to Host with Static IP

I have a Windows 7 host coected to a router ruing DD-WRT. The router is ruing a DHCP server.

For reasons I don't need to detail here, I have set a static IP on the host, as opposed to configuring a static IP reservation for that host in the router.

The IP is within the range of IPs the router is configured to hand out, it is not reserved, and it is not in use by any other host.

I have noticed that sometimes the host and the router can talk, and sometimes they can't. I haven't been able to characterize when they can and caot talk.

Is this just an idiosyncracy of the combination of implementations I'm using? Or is there something in the RFCs that states that if a router offers DHCP, it should ignore hosts it did not give a lease to, even if the IP the host is using is valid and available?