How can I defend against Pokémon Cinccino “Fluffy Tail”
You should be flipping a coin between every turn whenever a Pokémon of yours is asleep.
On Heads, it wakes up, so you have a 50%  chance of being able to use your Pokémon, and only on a Tails would you need any special items.

Asleep
Turn the Pokémon counterclockwise to show that it is Asleep.
If a Pokémon is Asleep, it cannot attack or retreat. Between turns, flip a coin. If you flip heads, the Pokémon wakes up (turn the card right-side up), but if you flip tails, it stays Asleep.

emphasis added

In a comment, it is noted that excess difficulty may arise from flipping a coin between &quot;rounds&quot; instead of between turns (i.e. after every second turn, not every turn). As Pokémon TCG has no concept of rounds, only turns, this should make it much easier to have an active Pokémon that is awake at the start of the turn, without using Trainer Cards or other effects.