It's not exactly the same, but I worked for the woman who was my pediatrician for a year one time and 3 years another time. Never could call her by her first name. Every time I started to, I thought I was going to pass out. That being said, I rarely saw her on social occasions.

I think what Soccer Mom said about maybe it was about confirming the end of the therapeutic relationship probably has a lot of validity.

Maybe if you start calling her by her first name, after a while, it'll feel natural. Or you could start by switching from "Dr." to "Ms."