Is it worth maintaining a friendship / platonic relationship with a person you are attracted to and would like to be more just friends, but who doesn’t feel the same about you? The answer to this question depends on why you want to continue being friends with that person you find romantically desirable, who doesn’t reciprocate your feelings and who seems to wan to stay in a friends zone. If you find that friendship to be genuinely important to you regardless of whether it develops into something else, because you have known each other for a long time, have a lot in common, find each other’s company to be stimulating, have a rare intellectual connection with each other, etc., and you believe you can handle being around him/her while knowing that there is no chance to turn it into more than friendship, then it might be worth maintaining that relationship.
However, if the only reason you are friends with that other person is because you harbor hope that maybe one day he/she will become romantically interested in you, and you plan to just hang around until it happens, it is likely to be a demoralizing experience. Few things will hurt your self esteem more than being interested in someone who is not interested in you, and who also seem to be interested in someone else at the same time. You should not be subjecting yourself to situations where you want someone who doesn’t want you, and you can’t help but show it or be upset about it not being mutual.
Of course, it is not easy to stop talking to someone for just that one reason – because you want to be more than friends, but there is a right and courteous way to do it – to be open and honest about it. If you don’t feel comfortable being around the object of your affection, you should simply come out and say it: “I really like you, but it’s hard for me being friends with you, because I want to be more than friends, but you obviously don’t. I have to stop seeing you or talking for at least some time until I get over this” or something along those lines. And then you follow through with that plan.
And, if it so happens that the other person realizes that they are interested in you as well, they will know what to do in order to contact you and let you know how they feel about you. But first, you have to be honest with yourself about why you want to be friends with that person in the first place.