The 1931-S is a very interesting coin. The original mintage of 1,200,000 makes it the second lowest mintage Buffalo nickel, after the 1926-S (970,000 originally minted). But the 1931-S is rare in circulated grades but not that rare in mint state. By 1930, some pioneering dealers, such as PCGS CoinFacts Coin Dealer Hall of Fame member Wayte Raymond, had starting saving original uncirculated rolls of newly minted coins. Mintage was a big factor in the decision making process. The 1931-S Buffalo was such a low mintage that quite a few uncirculated specimens were put away in the year of issue. In fact, there may be more uncirculated examples in existence than circulated ones. (This low mintage saving phenominum was repeated years later with the 1950-D Jeffereson nickel, another issue that's rarer circulated than uncirculated.) The very late dates, i.e. the 1936-1938 issues, are much more plentiful in mint state than the 1931-S, but other than that, the 1931-S is just not that tough to find. The mint state survivors usually have a decent strike and luster can be quite frosty. Interestingly, while fairly common in Gem MS65, the 1931-S is somewhat scarce in MS66, and nearly impossible to find in MS67.
According to a notice in the June 1934 issue of The Numismatist (p. 416), collectors could still purchase Uncirculated 1931-S Buffalo Nickels directly from the U.S. Treasury for "the face value of the coins and an amount sufficient to cover the mail charrges by first-class mail."