Voltage drop in that #12 is not a problem for the couple of amps those lights are drawing. Are those the cheepo fluorescents with the cylindrical starters protruding through the housing? If so, I would guess that the starter is shot. Fluorescents with bad starters (or even bad ballasts) will often still light when everything is warm (fresh from a hot work van) but may not want to relight after a cool down period. However, if both lights are doing the same thing then it seems unlikely that both starters/ballasts came bad from the factory.
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