iPad Air with iOS 9.0.1 freezes with Apple logo on boot, full restore does not help

I upgraded my iPad Air (MD792HC/A) to iOS 9.0.1 (13A404) via Settings/General/Software Update. The process went smoothly, but when the system restarted, the boot process hang with just the Apple logo on screen: nothing happened for at least an hour.

Having no other option, I started a standard restore/update process using USB cable and iTunes. I tried both the update and the restore, several times, with limited success. Normally, after the update/restore process, the system was unable to boot, with the same symptoms described above. In these cases I had to start the restore/update again. But in some cases, I sort of succeeded, I got a working iPad, but only until I switched it off. In most cases it could not start again.

I'm both annoyed and puzzled. I do not believe that my iPad is defective since I haven't had any problem before this 9.0.1 update. (as I recall, I upgraded directly from 8.x, skipping the few-days-long-available 9.0 version). Reading the bad upgrade experiences with iOS 9.0, I believe that I have an iOS issue, but I did not find anyone with a problem similar to mine. The USB cable + iTunes restore seems to be the last suggestion for the cases when everything else fail. But in my case, this fails, too.

Do you have any idea what is wrong here and what I can do? If I don't want to wait until the next upgrade, downgrading to iOS 8.x seems to be my only option...

Thanks,

Tamás