IIRC it keeps the IP address for as long as the DHCP lease is valid, whereas Windows will do a full DHCP request on every reconnect. That's perfectly valid behavior, and DHCP servers should not delete reservations before the lease expires - which doesn't stop some particularly shoddy implementations from doing so. Cheap SOHO routers tend to not persist leases on the flash to not use up NAND rewrite cycles, so they reset everything upon reboot.