Why wont my enemy go through the "hit" Animation and lose health?

This is the easiest way to fix the problem. Add a condition to the slimes chase event making sure it isn't either hit or death.

Basically what is going on is, you are subtracting the slime life after the hit animation is finished. However, the line of sight event is happening every tick and changing the animation to run before the hit animation can finish. Since the hit animation never reaches the end, the on animation finished event is never triggered.