Is it right to keep continuing a relationship even though there's no future together?

My boyfriend and I have been together since a little over a year. We were attracted to each other from the start and had become very committed right from the beginning. After 6 months we started having a lot of fights, cause of misunderstandings and behaviour differences, but we always resolve them and go back to normal again.

What I'm worried about now is that even though it was clear that we couldn't marry each other (cause we come from different social classes) we have been still together. And we do love each a lot. But I don't know if it's right to keep continuing this, because we both know that it's not gonna happen.

Sometimes I feel like both of us are living in denial. What would you suggest me to do? Or what would you have done if you were in the same situation as me?

Is it right to keep continuing a relationship even though there's no future together?
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