Gillette invented inexpensive safety razor in the 1890's, so anyone can be clean shaven without a butler or a barber. Their ads certainly encourages men to shave. Having facial hair now has a stigma of being either old or being an immigrant (or worse, according to One Thousand Beards: A Cultural History of Facial Hair, distinct facial hair made several dictators famous, such as Hitler, Stalin, Castro, Ho Chi Minh etc.). This Gillette ad made it clear that not being clean shaven is unprofessional.

In addition, prominent figures such as early film actors and even the Prince of Wales are seen with clean shaven face, and they also influenced the decline of facial hair.

It's not so much that facial hair fell out of fashion for elected officials, but more that photographs of presidents reflect the reality that facial hair has not been seen as serious for some time. The facial hair you see in those photographs generally represents acceptable, unmarked adult facial hair styles of the day. Men of the 18th and early 19th century were supposed to be clean-shaven, with sideburns eventually creeping down, and then neat mustaches becoming popular with young, fashionable men in the 1830s and 1840s; as they grew older, the mustache became acceptable for older men along with them. During the middle of the century, some odd beard styles were worn - long chinbeards, mutton chops, Amish-style beards on the neck, Lincoln's - without connoting anything other than "steady gentleman", although they look very provincial and farmerish to us today. This was followed by the more all-over beard, until it shrank back to the large mustache around the turn of the century, and then we're back to clean-shaven, which persisted during the 20th century.

Of course, not all men have been clean shaven during the 20th century. There have been fads for various styles, but they've been mostly associated with youth. Natty Clark Gable or Errol Flynn mustaches during the 1930s and 1940s were somewhat daring, and during the 1950s and '60s goatees and beards were associated with the counterculture. In the '90s, there were soul patches and goatees, and today there's designer stubble and all kinds of beards and mustaches, but all of these were/are associated with different groups: artists, twenty/thirty-somethings, hipsters. None of these groups really cross over with the group of men who run for president, and their styles don't say "steady gentleman" to most viewers.

Lincoln only grew his beard for his inauguration; he campaigned (and won) clean-shaven - something mentioned in this prior discussion of presidential beards. (It's a cute story - a little girl wrote him and told him he'd look more fetching with whiskers.)

I'm not sure Lincoln's beard is really "full" - he's a bit scant next to Rutherford B. Hayes, or even James Garfield.

In the mid-1800s, beards became linked with the healthy vitality of a natural lifestyle. Prior to that, they were considered eccentric or worse.

Edit, because I a word.