Thanks for the reply. I could've sworn I tried that and it didn't work: the Axe was on at the time, and Audio/MIDI setup was showing it as available as a separate device but not part of the aggregate device I'd previously associated it with. It was almost as if the Axe was registering itself using some sort of different UDID than it had previously, but that doesn't seem likely. It seemed more likely due to not powering things up in the proper order. My computer is always on, the Axe considerably less so, with Cubase somewhere in between (again, with various interfaces).
Probably what would best address it is to always use the aggregate device (regardless of whether I plan to use it), and always ensure the Axe is on before launching Cubase.