The type of love the OP is searching for is different than what you described Tree. Rainbow is writing from feelings of child need and desire. The writing comes from wanting more than just the T-client relationship.

The reality of the situation is: when the $$ runs out or the therapist retires, or something arises in the therapist's family requiring the therapist to stop working, the "relationship" with the client ends.
The "love and caring" is not unconditional. It is a business, and each client is part of that business. T's keep notes about sessions to remind them about you, to protect them from you, and to keep it a business.

T's can absolutely have a relationship with a client; the relationship is a proven tool in the success of therapy. But the relationship is a business one.

People can goto therapy for whatever they want. Just pointing out that if the OP has been in therapy over and over and over trying to "find love," maybe the OP should start looking around her and questioning that instead of trying to get a T to "love her."

peace.