Okay I noticed various things in your cap:
First of all you have an always event which rounds the X and Y position of the player. I don't really know why it's in there in the first place. I can imagine it would cause quite some problems and I'd really recommend to remove it.
That might be my fault
Looks like it's based off of the old versions of my tutorials. I had a very flimsy reason for doing the roundX, roundY thing. I've since updated them.
Anyway, it appears that the roundY bit was messing up your falling animation, delete those rounding actions and it works great.
Then you have the platform movement assigned to the player sprite itself. You might want to use a simple rectangle dummy sprite to have the platform behavior and add the actual player with animations and all on top of that.
He doesn't need to! He's using bounding box collisions and his sprite frame size is always 16x16... it'll be fine