From top to bottom, the U.S. government was over Morgan dollars by 1903. That may sound harsh, but have you ever tried to find a place to put 500 million Morgan dollars? The officials of the day were not the least bit enthusiastic about producing even a single additional Morgan dollar.
Coin collecting was alive and well in 1903. In fact, it is thought to be the year the legendary dealer B. Max Mehl ran his first advertisement. However, the collecting that was being done was primarily of dates and not dates and mintmarks.
The year was marked by great enthusiasm over the release of the first ever gold commemorative dollars to mark the centennial of the Louisiana Purchase. In fact, Farran
Zerbe of the American Numismatic Association was the lead of the project, but he was a bit more enthusiastic than the public. A total of 125,000 were made of each of the two designs and all but 17,500 of each ended up being melted.
All things considered, it is unrealistic to expect that the 1,241,000 mintage of the 1903-S Morgan dollar would touch off a mad dash to acquire an example. In fact, no one even expected a 1903-S Morgan dollar mintage, and with good reason. As The Numismatist reported, “Up to April 6th  the San Francisco Mint had coined in silver only half dollars. Quarters and dimes will probably be struck later in the year, but it is quite likely that no dollars will be issued at this mint during 1903.” But in June 500,000 1903-S Morgan dollars were produced, and more followed.
What happened to these 1,241,000 1903-S dollars has been a matter of debate for some time. There is an assortment of possibilities. There is no doubt that many were simply placed in the vaults at San Francisco as they certainly were not needed for commercial purposes.
Were some melted in the Pittman Act melting of 1918? The answer is almost certainly yes. We cannot be sure how many, but it is awfully hard to account for anything close to the mintage today based on what we know of other releases.
Certainly some examples were released over time. There was apparently something of a stir in late 1953 when some bags emerged. According to Q. David Bowers in his book, The Official Red Book of Morgan Silver Dollars, a bag was obtained by California dealer John Skubis, and there were other sporadic reports of bags but never many. Bowers concludes that by the late 1950s all were gone, which means there were no additional supplies in the Treasury holdings, the Redfield Hoard or other holdings where San Francisco dollars would be expected. This is typical of the differing nature of Morgan dollar fates as the 1902-S had a very similar mintage yet it is much more available. Of course, the 1902-S was sometimes lightly struck while the 1903-S was usually well-struck.
The lack of supply shows in today’s prices. In VG-8, where you expect prices of $30, the 1903-S is at $95. It is very elusive in MS-60 as is seen in its price of $3,950, and an MS-65 is $11,750. This suggests that there are poor supplies in Mint State.
Exactly what happened to the 1903-S will probably always be a mystery. Realistically it was very likely a combination of factors such as Pittman Act melting, being released and not saved and having $1,000 bags end up in the hands of people with little or no numismatic interest.