Figured it out. Turns out yesterdays DB maintenance caused a bunch of app servers to go into an in-between state where they kept failing. Fixed it but I need to investigate how to prevent it from happening again.
Update: Unsaved stories appeared to stay unsaved on the iOS side, and closing and reopening NewsBlur in Safari seemed to bring things back into sync. I'm considering this ticket closed unless the issue pops up again and I can't work around it.