I contacted support via email at about the same time I posted to the forums. They quickly shipped out a replacement battery and it just arrived yesterday. The new battery seems to have solved the problem. I would guess, from the lack of similar accounts on the forum, that this was an isolated incidence of battery failure.
I appreciate the responsiveness of the Purism support team in helping me solve this issue.
For the future, I would suggest considering other shipping methods, or giving the option to upgrade the shipping method. FedEx Ground is extremely slow when the destination is on the opposite coast. It took a little over a week from when I reported the problem to when the replacement arrived.