Amphibian Downpour + Creatures with Persist

Endbringer

I had an Amphibian Downpour out and my opponent cast Kitchen Finks and it immediately was destroyed and came back onto the battlefield but it did not gain finality and instead went into an endless loop coming back in and dying and coming back in and dying, giving my opponent 15 life over and over until the timer ran out at which point the Finks still remained on the battlefield and still didn't get finality. On the next turn, my opponent cast the red and black creature with persist that does 8 damage (I forget it's name) and it proceed to continuously revive and take down my entire life total, 8 damage after 8 damage over and over.