I think she probably does care for you a great deal but professionally she must indicate she only does so within the confines of your sessions. I suggest this is a boundary thing. It could be possible that showing affection has in the past backfired. She may be declaring her boundaries for your own protection as well as hers. This is a great subject to open up for discussion. Let her know then you need to know that your are more than a name for an appointment and that you need her concerns for you to extend beyond your sessions.