That answer is perhaps one hundred, two hundred three hundred or more years. Look how long the paintings of the old masters have been around.
Oil paintings have two natural enemies that can quicken their demise. The first is constant exposure to bright light, either direct or indirect sunlight or over-exposure to too bright man made light. The second enemy is high humidity. Remove both of these from the equation and a modern oil painting should last just as long as any by the old masters.
