USBKeyboard.h occasionally hangs

I was unaware that USB was so voltage sensitive.

You said yourself that the 3.9 and 3.3 zener diodes didn't work.

I tried out your sketch on my own version of that circuit (changing it to send the letter "a" so I could see it). It output "a" hundreds of times without hanging.

On your photo, I can't see the USB ground connected to your circuit ground. Is it?