My brother failed to save before battling the legendary (Groudon), and saved afterwards when his team had been wiped out by Groudon. Upon returning to the Cave of Origin, to the same spot that Groudon first spawned, he is not there. What can be done to make him respawn so he can be battled again, in order to advance in the story?
If you got wiped out by your legendary during the story, renter the Cave of Origin. On the second floor when going down, there is the normal stair-case, as well as another entrance to the west. Take the entrance and keep going downwards that way. You should eventually be able to encounter your respective legendary in another room.
Source: thanks to the user "[Dark Star] Greninja" on pokemondb.
Where you find Groudon is when it takes you somewhere and you battle its Primal form, right? If memory serves me right there's another way you can go in the cave that leads to where the actual fight happens. This other way is blocked off until Groudon/Kyogre take you to where the actual battle occurs but since you've done that scene it should be fine.