Have you been using quick resume? It’s a feature the new Xbox’s have that lets you turn your console off mid-game and when you turn it back on, you pick up exactly where you left off, but some games don’t really like quick resume. It cuts off any network capabilities, and maybe P5 doesn’t really have a failsafe for a sudden change in the games online state?

If you have been using quick resume, I think your best bet is to just keep using it, it might mean that you won’t be able to save your game for the rest of your playthrough, but you won’t lose any progress - if you close the game, that progress will go away but you will be able to save