Can they physiologically not hear the beat due to hearing issues or are they just not able to count the music on the proper beats?

I think for me it was posture.  I have had scoliosis and kyphosis since I was a teenager.  Martial Arts kept it from getting worse, but when I started dancing, I would think I'm standing straight from my POV but I would actually be lilting a bit to one side, which I would only notice when my teacher would actually correct it. 

I try to teach my students to look at the moves that make up a pattern or routine as lego bricks or letters in the alphabet.  So yes I am going to show a routine that will be my creation to help them remember- but just like with legos they can move and rearrange the pieces.  I have also found that writing down the pattern helps you memorize it.  it can be challenging to actually write out the moves and that help cement it in your brain.