Sometimes it just isn't convenient to use a static IP. For instance, if you want to be able to use DHCP in other locations with the laptop, setting it to static at home quickly becomes a real pain.
A better approach would be to set a reservation in the DHCP server so that it always issues a specific IP to a specific MAC address. That way, the laptop would always get the same IP.
However, I believe the problem is at least partly due to whatever cheapo router is being used. They aren't exactly known for having good software internally, many of them do nutty stuff. That's why I retired my old D-link at home and put together a firewall out of an old Compaq small form factor desktop PC, two network cards and
m0n0wall. Works like a charm.