Part of the problem is that it is so exposed - it's not very thick, and there's not much under it. So, water can get in there and do some serious damage. Gravity does the rest.
Presumably, the Numenoreans were clever enough to build their structures with drainage built-in, so they could reduce erosion that way. The main causes of erosion are going to be wind, water, gravity and chemical. This walkway looks as though it suffers from all of them (except possibly wind, which is worse when sand is in the mix). Chemical is going to be a mess when you've got rusty steel rebar around.
If you build with solid hard rocks, you're going to find that they last much longer than an amalgm of soft rocks. I don't think Tolkien specifies what type of stone is used in most constructions - he's certainly a lot more vague than he is with the flora!
But nothing is weather-proof in the long run; time will "grind high mountains down." That's why Moria, even though dwarf-built, shows quite a few places where the structure is crumbling or broken. The tower on Amon Sûl is long gone. He has Gimli point out the old and new stonework in Minas Tirith to show that the construction of the city is not static. In general, Tolkien is fair with nothing lasting indefinitely without maintenance. There are a few exceptions - the road the Rohirrim take (that Ghân-buri-Ghân knows about) is through a wooded area, and it is not clear why the trees have not taken over the road in the intervening years. The stairs of Cirith Ungol would have been built during the Third Age, but still are very old. The fact that they were in such good shape suggests that Sauron maintains them. It is, after all, the quickest way to get from Minas Morgul to the Tower just on the other side of the mountain.
Incidentally, Tolkien understood erosion quite well. I once went through the Hobbit and pulled out ten passages that described different aspects of it for use with an earth science class. Even the Carrock is geologically sound
![Wink ;)](./images/smilies/icon_wink.gif)
(Well, if you allow for glaciers rather than giants.)