C2 host it (or technically I guess pay for a company to host it), and obviously their staff have admin rights within phpBB. Day-to-day it's run by Citroen (who does most of the spam work as well as being an active part of the forum) and me. I mostly work on deleting spam/suspicious accounts, as well as more general spam duties. I can control much of the configuration of the forum (i.e. pretty much anything that sits 'inside' the software) but I have no access to the database or 'outside' the software, including doing software updates.
My guess is that a recent change to the database made by the hosting company to fix a broader access error has caused this, which means it's outside my control (I've checked the settings and see nothing relevant, nor would I expect that given that the config hasn't changed for months/years). I've passed the issue on to C2, which is unfortunately all I can do.