This is probably due to purely practical limitations - with almost no maps or written descriptions of foreign areas people had no way to pass down the tradition except by going there and pointing out the mountain.
Josephus apparently still had a tradition, as he gives a description of the mountain, but note how even with is description it can be hard to identify the mountain:
Josephus wrote that "Moses went up to a mountain that lay between Egypt and Arabia, which was called Sinai." Josephus says that Sinai is "the highest of all the mountains thereabout," and is "the highest of all the mountains that are in that country, and is not only very difficult to be ascended by men, on account of its vast altitude but because of the sharpness of its precipices".
This was still at a time when it was a few days walk for most Jews to go see the mountain, and it seems like the tradition was there but already unclear. After the destruction of the Temple there would really be no way to pass down the trasition.