Magnets

I'm familiar with the magnets demagnetizing from the entropy taking over (?), but other than that is there any way for a magnet to lose strength? I still don't get where the magnet gets the energy to move the object. For it to exert a force, doesn't something else have to lose energy? (Or mass, but I don't think magnets are performing matter->energy conversions.) What loses energy?

The concept of how an electromagnetic field exist is what I don't understand, I think.

Potential Energy. The Electromagnetic Force converts Potential Energy to Kinetic Energy is the simplest way to put it, I guess.

Consider gravity; an object at a certain height will have a certain Potential Energy, the equal of which is the total Kinetic Energy it could have after being accelerated. The higher an object is from ground level, the more Potential Energy it contains. The concept is that Energy had to be exerted to raise the object to that height. The same amount of Energy will be exerted to return it to its original location, i.e. ground level. A free falling object loses its Potential Energy and gains Kinetic Energy.