It's a clogged sink overflow drain.
I'm with Jadnashua on this one.
I regularily have to clear the overflow drain on my bathroom sinks to keep them draining properly.
But, I don't think it's an air LOCK issue. From what I can see, if the overflow drain is clogged, then when you pull the plug on a full sink of water, the air that was under the plug gets compressed under the clog in the overflow drain.
As the water drains out of the sink, the pressure on that compressed air diminishes and it starts expanding into the sink drain, thereby pinching off the water flow. Watch closely, and if you see the drainage rate slow to a crawl, and then see a big bubble come out of the drain, and then the sink drains quickly again, it's definitely a clogged overflow drain.
I have a special 1 1/4 inch trap adapter that's cemented directly into a removable cap. I put a 5 gallon pail under the sink, put a board across that pail, and then put that special adapter on the sink drain, and tighten the nut at the top so it doesnt' leak. Then I fill the sink full with water until the water covers the overflow drain and plunger the sink. Since the water can't drain, the water surge goes through the overflow drain, and I end up plungering all the rotting putrifaction in the overflow drain into the sink through the overflow drain hole. Then I remove the board, take the removable cap off the bottom of my trap adapter and the water and crap in the sink drain into my pail. Then I'm good for a long time again.