Any couple who has been together for a period of consecutive years will tell you that some degrees of individuality become replaced by the things that make one a "couple" over time. While some may see the gradual enmeshment of couplehood as a loss of self and, thus, a negative aspect of relationships, couples who would describe themselves as happily married (partnered/cohabitating/committed) have most likely discovered one of the key elements of any relationship: the art of compromise.
When relationships dissolve it is usually due to some kind of seemingly unsolvable conflict. While "irreconcilable differences" commonly exist among humans, it is absolutely a choice to not find a middle ground that both parties can live with. Choosing to end a relationship is sometimes the healthiest thing we can do for ourselves. All relationships are rife with conflict; individual needs will inevitably be in opposition with one another at some point. It is the ability to learn to gracefully navigate our differences as people that give our relationships meaning and stability. This is never more true than in the relationships we form by pure choice, especially to those whom we commit in word or ceremony.
While any form of compromise means sacrificing one's own needs and desires in some form to accommodate another, it is certainly possible to find happiness with this mindset and not feel as though one has given up parts of oneself in order to make another happy. A 2014 study (Lin, et. al.) found that those in relationships who had a relational focus, that is, commonly used the "we" pronoun, rated themselves with a higher subjective happiness than those who were more individually focused. It is not the giving up of self that creates happiness. The skill to compromise is not merely enough to assume happiness in our relationships. Rather it is the context through which we view our relational experiences that increases our sense of well-being.
All of mankind has the ability to pursue happiness for the self. But if each person is seeking to create individual happiness, one may never find the happiness that could exist through meaningful relationships if we do not first consider the importance of shared meaning, nurturing one another and realizing that relationships are ultimately what make us human. To try to live outside of what is good for the relationship is to try to live a solitary existence. Happy couples usually are so because the word "couple" is not just a way to describe the relationship. It is the essence of the relationship.