Would Mespirit respawn if I beat the elite 4 again? I saved my progress after he died and he's not showing up in nameless cave at all.
All legendaries should respawn after defeating the league, but this may take up to 24 hours after beating The Elite 4. I do not advise fiddling with your 3DS clock, as this may cause issues. However, Mespirit has requirements to appear in the first place.
For Mespirit, you must interact with the portal in the nameless cave between 04:00 and 19:59. Additionaly, three Pokémon with max Happiness need to be on your team.
You can raise happiness through multiple means, such as giving them a massage in Mauville, or leveling them up, source here.