In the Exploding Kittens game, the rules say
You won't ever run out of cards in the Draw Pile, so there is never any need for a reshuffle.
In every game I've played all the cards end up on the discard pile fairly quickly and there is nothing left in the draw pile, so we have to reuse them.
Is this meant to happen? Are we doing something wrong?
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.
You are likely misunderstanding a rule or two. However without more information I can only guess what that rule might be.
You start the game with N-1 exploding kitten cards in the deck (where N is the number of players).
Exploding kitten cards never get put in your hand. When you draw one if have a defuse you get to put back in the deck. If not you blow up and are out of the game.
There should be no way for you to go through the whole deck without all but one person exploding.
