Most Miata owners eventually have power window problems. It might be a window that goes only partway down, or one that goes up slowly. Some of these problems can be fixed by the owner.
Dirt sometimes builds up in the guide channel beside the small vent window. Clean the channel with a cotton swab and denatured alcohol, then use another swab to apply lubricating grease that is safe for silicone or rubber.
If both windows stop and the motors do not run, check the fusebox. Look for a fuse labelled either "POWER WIND (30A)" or "P.WIND (30A)." If it is blown, replace it.
The window motors use cables to raise and lower the windows. Sometimes the cables break or simply slip off their pulleys. This fix requires removing the door panel. Note: If you hold the switch on and the motor continues to run after the window stops, the cable is probably broken.
The contacts in the window switches get dirty. The switches need to be either disassembled and cleaned, or replaced.
Major Electrical Failure
Sometimes window motors or regulators fail. Unless you feel very confident of your ability as a mechanic, this is a job best left for a professional auto repair shop.