Running out of cards in Exploding Kittens
You are missing a critical step.  Every time an Exploding Kitten is drawn it needs to go back into the deck if it is defused.

From the rules:


  Defuse:
  
  If you drew an Exploding Kitten, you can play this card instead of dying. Place your Defuse card in the Discard Pile. 
  
  Then take the Exploding Kitten, and without reordering or viewing the other cards, secretly put it back in the Draw Pile anywhere you’d like. 


As long as you do that, and you had the correct number of exploding kittens in your starting deck (1 less than the number of players) the deck will never run out.