Aside any scientific explanation, like in "The Happening", about the events of the beach, these movie is easy to set in the Supernatural Universe. A beach that shortens the lives of it's 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.
As noted on the Headscratchers page, the menstrual cycle makes no sense: if it moves as quickly as aging, females 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.