When a relationship is formed, all different appealing aspects of the person are brought into view; their charm, their hobbies, their interests, their personality, and their openness. All of these traits of the person, in play with your own, can make for a fun, vibrant, and trusting exchange of emotions and trust. However, as time progresses, things that made your partner's persona appealing may tend to lose their magnetism. In other words, things that may have drawn the person to you originally will not be as prominent as they once were. Instead, it will come to the point where one partner, usually ahead of the other's time, will evaluate the relationship based on what they do not relate to in the other person.
That being said, when faced with noticing that your partner no longer sees the potential in the relationship that you would like it to have, you must ask yourself: Do you not want to lose this person? Or do you not want to lose this relationship?
I understand that this is a frightening and overwhelming question to ask yourself; I have asked it to myself before in my life. The most painful, yet awakening part for me was seeing that my partner was in a position where zie was asking him/herself the same question (I'm trying to avoid gender-based pronouns).
If this is the case for you, having your partner try to change his/her mind may not be the most healthy or worthwhile option. It is fair to say that before zie approached you with this objective, zie had been wrestling with the thought for some time before having built the courage to approach you about it. Trying to change their opinion will only make it harder for them, which in turn, will make it harder for you.