Such an interesting thread...
I will share my own experience, more on the relationship with escorts than SR (I only had one SR)
When I start seeing a girl many (many) time I tend to end up in a grey area.
In the most extreme case it can be falling deeply in love. I do agree with
@MikeH , you need to let it go consciously for it to happen. In the only occurrence where I fell in love, I had a conversation first about my dilemma to let it go with her. She told me life is too short to not enjoy such an amazing feeling, I kind of agreed and fell hard... It didn't end really well but I cannot regret any second of this passion as it was so intense and created lifetime memories.
In a few other occasions, I felt the need to see some girls more and more and kind of built a mental barrier to avoid creating a too strong attachment. The best way to do so is definitely to see each other less or cut short the relationship.
I'm mentioning cases where there are reciprocal feelings. If not, it sounds really bad guys. Letting someone with a material agenda being under your skin is the perfect recipe for disaster. I don't want to be jugemental at all. I'm more thinking about your own good and I know first-hand you cannot reason with your feelings. In any case, it is quite obvious the right course of action is to end the relationship, to delete any email address and phone number and go to the gym or getting out with friends and family. I'm not saying it's easy to do...