If the counter is working, then the problem is clearly with the text updating. The only solution I can think of with the given information is to make sure you are setting the KillCounter text to the instance of the text in the scene and not to the prefab itself.
On a side note, I noticed that you are repeatedly setting the text to the score in Update(), which is not performant. I would only update the text immediately after you change the value of the EnemiesKilled variable: