I'm just sending back my SECOND D800. Both have had the 10-pin connector recede into the body upon first use.
If you don't have a remote, but want to check your connector before you run out of warranty, just press your pinky finger on the connector and see if it recedes into the body at all. If you feel it move, even a little, it will break when you try to press or screw your remote cord into it.
This is what it looks like when it fails:
I bought my first defective d800 on January 24 from B&H. My second one arrived last week, and was also defective on first use. I am a pro shooter, and have used the same remote on my D3 hundreds, if not a thousand times in the past five years, with no problems. I mention this in way of assuring anyone that this is not a 'user error' problem, it's a manufacturing defect, or possibly a design defect.
I personally feel it's important, if you already own a D800, to test this connection before you run out of warranty.
As an aside, on my first D800, the first time I popped up the flash, a screw fell out and one of the arms popped off. I found the screw and re-assembled it - If there were a way to DIY this socket problem, I'd be all over it (I can't afford to take two months to acquire a new camera, which is what's happening now).
Check your cameras, and have them repaired under warranty while you can... I hope my next one is not 'strike three'.