In another question I asked, I confirmed that you can encounter the Weather Genies again without doing the Pokeleague, even if you faint them or run away. Does this also work with the Sinnoh Dragons? Or would I have to do the Pokeleague again to respawn them?
(Can't test this myself because I don't exactly have a spare Lake Trio or Palkia just chilling in my PC)
Yes, the Dimensional Rifts do respawn. Source: Some kind stranger on the GTS (named deadcns) gave me a free Lvl 100 shiny Palkia, Azelf, Uxie, and Mesprit with good natures (that totally were'nt hacked), so I stuffed them in my party and went into the rifts, knocked out the legends, and the rifts respawned after I landed and used the Eon Flute again.
To encounter them again after fainting them, you will have to defeat the Elite 4.