I know that wax is not soluble in water so I think it doesn't react with or dissolve in water-based solvent. Some sources I have consulted say that it does react but slowly. So getting confused by different opinion, I have no idea what the truth is.
Being insoluble in water does not mean something cannot react with water or water-based solvents.
Plant waxes are made up of a number of constituents; amoung them esters, alcohols, alkenes, fatty acids and carbonyls. Especially the esters can be hydrolysed by acidic conditions, creating a more hydrophilic area which water (and more acid) can use to penetrate the layer.
Another probable reason is the fact that acidic proton transfers often involve the release of heat which will make the wax layer less viscous. All these things taken together mean that slowly but surely, the wax layer will be destroyed given enough acid rain.