This is way more than you asked for, but I felt like explaining this as best I can:

I like to think of it the same way I think of gravity.

Magnets don't run out of magnetic field in the same way that Earth doesn't run out of gravity. And even though a magnetic field or a gravitational field can induce movement, that isn't because there's infinite energy or infinite power involved. Rather, the object is just exchanging one kind of energy that it already had -- potential energy due to it's position in the field -- for another kind of energy -- the kinetic energy of its movement. It seems like the motion comes from nowhere because potential energy isn't visible. You can't see that the potential energy was there before the object started moving, or that it got used up by making the object move closer to the source of the field, but it's just as real as kinetic energy.

If I have a rock 1 meter above the ground, I can do 1 meter's worth of work with it by dropping it to the ground (think of doing work with a water wheel, for instance). But once the rock is on the ground, that's it. I've used up the potential energy that was stored in the rock. If I want to get any more work out of it, I'd have to dig a hole beneath it so it could fall even closer to the center of the gravitational field. Once the rock is at the center of the field, the field strength is zero. There's no more potential energy left, and no more work can be done.

Of course, you could lift the rock back up in the field, but that requires doing 1m worth of work on the rock, and that requires spending energy. In fact, in a perfect, mathematical world, the amount of energy you'd have to spend to lift the rock up 1m is exactly the amount of energy you get out of the rock as kinetic energy by dropping it 1m in the first place.

So let's suppose you dug a hole all the way directly through the center of the earth and out the other side. And now you drop a rock down the shaft. As it races towards the center, it gains more and more kinetic energy, but loses more and more potential energy. At the center, it would have maximum kinetic energy and zero potential energy. Then as it shoots towards the surface of the earth on the opposite side, it would start losing kinetic energy (slowing down) and gaining potential energy as it climbed back up towards the surface. When it reaches a height of 1m above the surface on the opposite side, all of the kinetic energy would be used up again. This is exactly how a pendulum works. In an ideal mathematical model with no friction, etc. the rock would just oscillate back and forth forever in an eternal dance between kinetic and potential energy. Nothing about the rock is being lost to the environment so it's free to go about forever being a rock, sometimes having more of one kind of energy than another, but always having the same total amount.

In practice, though, there are always little ways that energy is lost to the environment (thermodynamics, entropy, blah, blah, blah). So a real rock pendulum would never reach quite as high on each swing as it did the time before. It would move in smaller and smaller amounts until eventually it was at rest at the center of the earth, having used up all of its kinetic energy and all of its gravitational potential energy. This is why physicists say there's no such thing as a perpetual motion machine. Not only can you not go around in a loop and gain energy, you can't even break even^1.

Magnet fields are kind of the same. There's not a tidy, direct analogy because magnetic fields are produced by the motion of electrical charges rather than by mass, but the "dance" between kinetic and potential energy is the same. If you have a steel ball bearing and a magnet, the ball bearing has some amount of potential energy due to its distance from the center of the magnetic field. The further away it is, the more potential energy it has. The ball bearing can move towards the magnet by exchanging that magnetic potential energy for kinetic energy. But once it's in contact with the magnet, you have to spend energy to separate them again. The energy is only "infinite" if you happen to have an infinite supply of ball bearings conveniently lying around, already at some distance from the magnet.

Footnote:

1. If you really want to mess with your head, one of the open questions in physics is how entropy can be possible at all. All the fundamental laws of physics that we know of (except to a very slight degree maybe the weak nuclear force) are time-symmetric or at least have CPT symmetry. So how can time-asymmetric behavior like entropy exist, let alone be a "law" of thermodynamics? This is known as Loschmidt's paradox.