What is the source of the Big Sur river?
This is the response I received after asking a friend who works as an Hydrologist:


  The river is fed by ground water that is slowly leaking out of the base of the mountains. Rain water slowly percolates through the (elevated) soil, which is why the river still runs many months after the rainy season.




Note to other prospective respondents: if you have a more technical/accurate answer to my question, I am still curious about the mechanics of this process, and am  will mark yours as the correct answer.