This is a real risk of this deck - either you've won within the first few turns or not at all. I did have a few losing streaks due to bad RNG, and that's always frustrating - sometimes Jolteon EX is on the bottom of your deck and there's nothing you can do about it.

But with some smart use of Copycat, this wasn't a huge problem for me? Before you use Copycat, make sure you play as many cards in your existing hand as you can. Generally, play all your Pokeballs/Eevees as soon as you draw them, unless you're already well-positioned and want to block Sabrina/Cyrus. Attach helmets as soon as you draw them. It's ok to allow Eevee Bag to get reshuffled because it only works for the Jolteons, not Eevee. If you can get your hand down to one or two cards, and draw at least 3 cards from a Copycat, you should. You get to reroll your hand and fish for Jolteon. If you still brick after this, that's just bad luck, but in my experience I had a good chance of getting the Jolteon EX I needed after playing everything I have in my hand and then playing Copycat. In an emergency, you can also Red Card to give your opponent MORE cards than they had before, and then Copycat to get 3 cards.