Marble is a type of limestone which is alkaline. Rainwater is usually acidic depending on how much acid it picks up from such things as coal-fired power plants and the like. Acids react with alkalines - or bases - and dissolve them. It's not as dramatic a reaction as baking soda and vinegar but over time it takes it's tol.
Marble is porous which is why it is not recommended for kitchen counters where it absorbs liquids and stains easily. Outdoors, there is just too much air pollution....yes, as mentioned, acid rain plus the mineral contaminates from blowing dust, gas contaminates automobile exhaust, etc.
eg-like that of taj mahal