Either the attack is bugged or you weren't moving in the direction you want to attack. If you stand still or are moving away from the enemy, you won't hit them. Also, you need to get the axe to kill them in 3 hits instead of 9 -- currently unclear, but it is in the shed to the left of the island; making some changes to make it a bit more clear.
I'm probably going to change it so that the attack button is a toggle, so you hold it down and then use the movement buttons to attack -- that way I can have shooting along with melee.
Anyway, thanks for playing and the feedback!