Let's take this concept a step further and say that ALL separation anxiety is due to "inner separation" whether or not there's a physical separation.
In other words, your child becomes anxious when s/he feels disconnected from you, and that feeling may be rooted in any type of separation — physical, mental, or spiritual — real or imagined.
If you believe you "have to" leave your child, your belief in lack of freedom will separate you from your Self. Your child will feel that disconnectedness even before you leave.
But when you achieve inner connectedness, it soothes anxieties AND makes it easier to attract into your life more people with whom your child feels a secure, consistent, loving connection. Creating such a "village" can lessen if not eliminate your child's separation anxiety.
So do your best to make peace with separations when they occur, and hold the vision that your child will be okay. But remain open to the possibility that your child can have all the physical closeness s/he desires, too.