My allay popped out of existence while I was watching it and went back to the nether. 
I had just transported it through the nether (about 1500 blocks nether-wise). Named, holding a torch, and leashed. As I was walking away from the portal, at a certain point my allay disappeared. I saved and reloaded to see if he'd pop back into existence but he didn't.
I went into the nether, through the portal I'd taken him through, and there he was.
I've included a video that shows when I first brought him out of the nether and he disappeared, finding him in the nether, and repeating it again (this time I tried unleashed, but he disappeared again)