I wish I was there with you two to listen to your conversation when you had your "talk"!
I can really understand your girlfriend's point of view. We don't just give her an additional option for sex when she starts seeing someone else, we also give her away to some extent and not all women are comfortable to shuttle between bedrooms. Some women prefer to have sex with just one man and given the choice many would choose the lover provided that some kind of intimacy with her steady partner remains.
I imagine that it must have been hard for her to sit you down to tell you how she felt about having sex with you. She would surely know that you felt strongly about having to reclaim her every time, while she increasingly felt that she didn't want you in her, at least not every time. You would probably have sensed already how she was losing interest. How she asked you to cum quick because she was sore or when she wanted to sleep overnight with him so that she could be just with him. It was courageous of her to openly discuss such a sensitive matter. I'm convinced that if a couple doesn't discuss it openly at some point, that it can affect the relationship in a more fundamental manner. So it was both courageous and good of her to open the discussion.
It goes to prove that our girlfriends and wives love us. They do not want to shortchange us. That said, in no relationship should one side feel obliged to have sex. How did you respond, other than that you simply agreed to stop having PIV sex. Did you guys still do it a last time? Did you perhaps try to negotiate some form of phasing out?
Either way, if a couple can take such a consequential decision together, then that is something really special.