I have several Fluxx versions. In all these versions, if keepers have powers, they can be used each turn (once during your turn). Exceptions are noted.

So I assume, Adventure Time Fluxx uses the same rules.

Also, I did not found anything that contradict this in the official rules.

In the official rules, it states:

If a keeper has a special power, you must have the card on the table in front of you in order to make use of the power.

So as long as you have the keeper in front of you on the table, you can use its power.