The magnet is not actually doing any work. It’s just getting pushed on, similarly to gravity or to a table holding a weight. The energy comes from the dynamo shaft pushing, and the magnet sort of acts like a magic lever converting that force on the shaft to a force on electrons instead.
Now, that said, magnets *do* wear out and lose magnetism. Sometimes over the span of seconds, other times over the span of centuries.
As long as they don’t get too hot or hit with too much impact or magnetism, magnets never lose their power. It is a property, like mass, but unlike mass (which can only be destroyed in nuclear reactions) magnetism can destroyed by high heat and a few other types of abuse. This also allows you to “add magnetism” to some metals to make them magnetic thereafter.
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