Pointer disappearing from screen after few seconds

This problem is most frequently associated with input devices like a trackpad or Magic Mouse - usually wireless devices. Your first course of action would be to replace the batteries. Even a wireless keyboard can exhibit skittish behavior if there's insufficient power.

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Depends if it does it in Finder or just in some applications. There are applications where the pointer will be dimmed out if you've not moved it for a few seconds. It should reappear immediately you move the mouse or touch the pad.