I'm no expert.....but if you were at JFK and you didn't hear anything for.....oh....lets say over a minute, wouldn't you check your mic button?
Many of the newer, general aviation radios and audio panels have a built-in stuck-mike protection that will automatically end a transmission if over 30 seconds (or some timeframe like that). Makes it somewhat tedious when filing a long-winded IFR flight plan or PIREP in the air but at least we are able to see this feature in action. It seems logical to me that the big aircraft would have this technology as well, but I don't know for sure.
Maybe the stuck mike was on the ATC-side? I recall at least two audio clips here as well as some actual experiences of ATC-side stuck mike examples.