The one for my 70-300 is touchy too - hard to get it on level as it should be without messing it up. I can't say for sure what the best answer to your problem is except that a few times I've accidentally bumped the hood to the point that it's fallen off - even on my 24-70! But I'm fairly sure that was when I had it screwed on the right way, whether it was reversed or not, I don't remember. It may have happened both ways.
Both hoods still work as they should and have not broken.
Did you try to unscrew it even though it's lopsided?
I don't have a 28-135 so I'm unfamiliar with that lens and hood.