A lot of people think that when you go to catch arceus in hall of origin, you only have 1 shot to catch it, so they save it beforehand.
but what if you forget to save it?
well, just on and try to catch it, and if you kill it, exit hall of origin and spear pillar and go back in and the flute should start playing, and when you let it play, the staircase should appear again, and when you get to hall of origin, arceus should be there again.
trust me, it works, and if you don't believe me, you can also save the game before you go up the stairs or when you reach the top of them.