In answer to your question, it would seem that some relationships can last, based on specific circumstances.
These circumstances are usually rooted in the active involvement of both parties involved. There are other factors to consider though, for example time and distance, which can be a deterrent to relationships if these things can not be compromised upon.
But again, if there is love, there is no obstacle than can stand between two people that are meant to be together.
Age and maturity also play a huge role in the outcome of a relationship. Sometimes, it can be a case of the right person at the wrong time. Often, it may seem like the relationship does not work because one or both parties is not emotionally mature enough, however, if there is deep-rooted love, sometimes time and space allow people to grow separately (which is imperative) and come back together later on in life.
This means there is always hope in love, and relationships can indeed last, even in ways that you don't expect them to.
There are different types of relationships, but if you are referring to romantic relationships, the ones that do last can turn into marriages which can in some cases last a life time.
If a relationships evolves into a marriage, this requires even more work to solidify it. Compromise and sacrifice is necessary in order to facilitate the unity between two people in a marriage, however, if there is love and both parties are willing to make it work, there is no reason why it shouldn't last.
Marriage can be a beautiful thing, and if you are truly lucky enough to find your soul mate, you will be grateful for all the hard work you've put in to make it last. Nobody says it's going to be easy, however, it will definitely be worth it!
To summarize, yes relationships do last - at least the right ones do, and the wrong ones will burn out. So there is no need to worry. The person that is meant for you will be in your life regardless, you just have to trust and have faith that when the time is right, the right person will present themselves in your life. Timing is everything.
I hope this helps.