After 5 months in a 4 year old home, water began leaking from our family room ceiling directly below the master shower. It happened a few more times, but only after the shower had been running for about 20 minutes.

I had a plumber come out to diagnose the problem and after cutting a hole in the ceiling downstairs, he saw water coming out of the hole in the OSB for the cold water line. He thought that a new closet install a few weeks prior nicked the line between the valve and the shower head (it only leaks when running). After tearing the drywall out in the closet, the leak is clearly not coming from there.

The only other thing I can think of is the drain. Can anyone explain why the pan / drain would leak only after twenty minutes of running?

"I had a plumber come out to diagnose the problem and after cutting a hole in the ceiling downstairs, he saw water coming out of the hole in the OSB for the cold water line."
For openers, please explain what a "OSB" is, ( Old Shower Base? ) and now tell me what kind of a shower enclosure you have. Custom tile? Manufactured shower enclosure? Plastic or fiberglass? There's no doubt in my mind that it's not a pressure leak so that would put your leak in the drain or if a custom tile job, the tile grout.
But until we know what you have we can't be of much help. Regards, tom

Tom,

Thanks for your quick response!

The OSB I referred to is the oriented strand board subfloor. Holes were drilled to run the supply lines down through the studs and subfloor, and then between the joists. I think the plumber saw the water coming out of the hole for the cold water line and assumed it was the line itself that was leaking. It appears that it is the easiest point of exit for the water that builds up under the shower pan.

The shower is a fiberglass base with custom tiling. There is still a solid bead of calk in the joints of the tile walls and glass walls but I cannot tell if the grout lines have been properly sealed.

I popped out the grate for the drain (as did the plumber) and could not find any problems from above.

Your plumber should have told you this. I don't see any way out of opening up sub floor and find out exactly where the leak originates. My bet's on the drain. But let's do some checking first. Does the floor of the base give a little when you step on it? If so and before you tear anything up check the lip of the drain for a ruptured seal. It could also be that the grout has shrunk and is letting a trickle of water leak down.
To check to see if you have a drain leak, pull the strainer and close the drain off. You can stuff wet rags down the drain or blow up a balloon inside the drain and block it that way. Now fill the base with a inch or so or water and check for leaks after 1/2 hour. No leaks? Now drain the water. If no leakes you've lucked out and don't have to mess with the sub floor. If you see a leak while draining the base then you have a leak in the trap or raiser and the sub floor will have to be opened up. Let me know what you've found after you have checked. Tom