Ok, it is obviously a flawed estimate. Hopefully it has long been since changed. Yes, it could happen that the connection closed 40 times. Far more likely is that it almost closed and became a one way trip for incoming water a few times. Right now the Strait of Gibraltar is so deep that it has large enough Reynolds number to allow two way flow of water in (salty) and out (more salty). Black Sea is the same. But in Caspian Sea, there was at least recently a lagoon that became landlocked except a river like flow.
http://en.wikipedia.org/wiki/Garabogazk%C3%B6l
This can go on indefinitely until the whole lagoon becomes filled with salt, or Caspian Sea runs out of salt as case may be. In the case of the Mediterranean, the oceans may not have enough salt to fill the sea, as it is a couple miles deep and huge. Some one else can do the math. So it could have closed only one time, though gradually enough to concentrate much salt and precipitate it out (only about 1/4 of the water content can be table salt before precipitation to the bottom or edges, iirc).
What is known is that huge salt flats developed and were covered by sediments, effectively sealing them under the ocean (like much of the Siberian Arctic Ocean covers a continental shelf that is thick with buried ice). The drilling teams found that in the 1960's as well as huge canyons in the delta sediments of the Nile and all the way up beyond the Aswan dam hundreds of miles upstream. So it did not indefinitely have a slow input.
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A doozy of a waterfall! Even today the Med is saltier than the Atlantic and in fact this saltier water is outflowing at Gibraltar in a layer below the less-salty inflowing Atlantic water.*
More recent information has pretty much disallowed this. The waterfall is either completely buried or non existent. From what I read, the current thought is that the gradient was so slight that it never scoured the bottom much before closing enough to carve canyons into the continental slope or shelves in the Mediterranean basin at the believed points of entry around Cartegena and Valencia. Considering you have a hundred miles and a gradient of maybe 20 feet, it could be a lazy flow down a huge Amazon. The flow was so broad and shallow, maybe 50 miles wide and a hundred miles long, that it never scoured enough to widen the flow. If tides were substantial at the inlet, then a huge tidal area would also cover up incipient little canyons. Land raised before that happened, again since it was so broad it happened gradually. Sorry. I wish it had a huge cataract as well.
