I will say this again. You should not cut a hole into the middle of a face! You are going to have problems. You are asking for advice and we are giving it to you. If you are going to ignore our advice I see no reason to continue trying to give it to you. lol

It's fine to cut the hole but you need to have and edge connecting to the outer edge of the face,

To prove this, Try to use split poly and split an edge to that hole you cut in figure A above. You will get an error message and maya will not let you do it! You have created what maya calls a "hole" and it is illegal geometry.