Magnetic fields aren't some kind of energy that can be sucked out of the magnet like a battery. It's more along the lines of how you can use Earth's gravity for power:
Hydroelectric power
does use gravity - but the water's got to get into the basin in the first place before it can then fall over a turbine, which is of course done by solar energy, via the water cycle. In that case, you can only get out,
at most, the amount of energy that was put into the water to move it up to the higher elevation in the holding basin above the turbine.
What makes magnets special is that they can influence electrons. Push a wire through a magnetic field, and the electrons will want to move a certain way as they pass through the field. If they're in a conductive material, this will permit the flow of charge, which is current. But while you're pushing the wire through the field, the moving charges will puff out their own little magnetic fields to try to return themselves to the original field state. If the electrons have nowhere to go though, if the wire isn't connected to any kind of load, then they can't move much, so their resisting magnetic field is very minimal. But if there's a load attached, they will resist more intensely - this is why a generator turbine needs to be forcibly pushed to keep spinning, and it's also (a small part of) why these "perpetual motion machines" can't exist.
More on magnets in general: They've got a field that acts over a large distance, at least when compared to the electric field, which is what keeps matter from passing through other matter. That field works over very short distances, such that we perceive it to be a sudden impact.
If you looked at a magnet on a different scale, it would react in very much the same way: Start 5 miles away from a small magnet's north pole, and walk toward it while holding another magnet with its north pole facing toward the stationary one. The vast majority of your journey will be quite uneventful, with the exception of the last few inches of the trip, when you are finally close enough to feel the magnet's effects. The electric field's range of influence is simply very small.
(And then you've got gravity, which operates over very large distances.
Maybe they're all even related...somehow.)
In either case, magnetic or electric, it's still just a static field, and it's not some kind of infinite energy source that the magnet is stubbornly trying to keep to itself.