Aside any scientific explanation, like in "The Happening", about the events of the beach, this movie is easy to set in the Supernatural Universe. A beach that shortens the lives of its visitors, could have many explanations that the Winchesters would speculate:
1) A ghost is possessing the beach, probably one of a vain person, who following the cheating of his spouse for a younger lover, killed himself by throwing himself into the sea. His spirit returns and starts sucking the age out of the visitors as revenge.
2) A deity is doing this (or a tulpa): imagine that that area was once a sacred path of a fertility god/goddess, who would give fertility to his followers expected human sacrifices... only not dead ones. It would have just sucked their youth and life essence until they died of old age.
3) The obvious course... a witch did it... this is the modus operandi of several Vain Sorceresses that need to retain their youth. And to joke a little, in other words: "It was Agatha All Along".
As noted on the Headscratchers page, the menstrual cycle makes no sense: if it moves as quickly as aging, girls would have periods every ~2 minutes, but if it works normally Kara's baby couldn't have been conceived so quickly. In this scenario, the cycle works normally, but the beach "knows" when conception is possible and therefore moves things along.
- For that same reason, bodies are aging faster but hair, fingernails, and metabolism is not moving at the same pace. The Beach is selectively accelerating processes that are much more existentially horrifying rather than annoying.
That many missing people at the same resort? The cop is unsurprised when the notebook corroborates the missing people from the past.