Raspberry Pi (or another device) suddenly not getting a DHCP address?

Tonight, after I made a couple changes to my wired in-house Gigabit network (I recently added a few Cat6 runs after moving my main Wireless router—in this case an AirPort Extreme base station), I noticed the Raspberry Pi webserver that was hosting wasn't reachable over the network, and Server started reporting an outage.

I have that particular device set using a DHCP Reservation based on it's MAC address, and it's been working like a champ for over a year. So something was strange, since I hadn't made any networking configuration changes on the Pi itself in a few months, nor had I unplugged it at all in the past month.