You have no idea what the military does, do you.
I think I have a pretty decent rough idea. So if all they do is loiter, remind me why they're spending about $1T on the F35???
The US military has evidently already rejected the idea, presumably because they prefer to spend their money on things that go faster (e.g. the said F35).
Loitering over enemy territory in something that may even be bigger than a barn strikes me as a seriously undesirable idea. It may be stealthy, but during daylight you'd have to be half blind not to see it with the naked eye. And given that it presumably needs to transmit to be useful, it can't really be stealthy anyway (unless, I suppose, it send everything upwards to satellites).
Autonomous drones strike me as a much safer way for that particular mission.
Airships are one of those ideas whose success is always just around the corner. They had a brief window in the 1930s, until the Hindenburg put paid to it, and then along came WWII to make large aeroplanes a practical reality.