I could have easily knocked it off accidentally as I was struggling to connect the short antenna connector through the styrofoam wall to the flight computer. Knocking this out prevents power from getting to the antenna, and hence the GPS would have trouble seeing satellites! The problem seems to be the issue, but I won't know for sure until I fix the connection and test some more.
Full picture of the flight computer with the inductor after the break.
UPDATE: I connected the joint where the inductor used to be with straight solder, and we're now back up and running, successfully receiving a GPS lock. I think losing the inductor may have actually improved reception!