I think the people who continue to have friendships through out their lives must have something others want, admire or aspire to like a sparkling personality, well connected network, great listener for those energy vampires or even a gorgeous holiday home. You are useful to them somehow, even if emotionally useful like you make them laugh or always have an interesting perspective on things, it doesn't have to so sinister.
They also Leave nothing to fester: genuinely can let A LOT slide, don't keep a score of who invited or called whom... etc. They give freely with very little expectation and are BOTH excellent at communication and ironing out misunderstandings. It helps living close or having a shared activity or interest that regularly brings you into contact like religion or sports. So I suppose, being generous, confident and interesting helps you keep friends for life.
Poor MH and stress is so prevalent many people don't have the headspace, energy or bandwidth to support new friends and their issues, only 'investing' in ones who are useful or have so much history with already because emotional support and time are finite resources, it makes people selective who they befriend.
I think the best approach is not to put all your eggs in a basket in one friend, keep meeting new people but only give as much or little as you can without feeling bitter or disappointed if it's not reciprocated. Be brave and invite them out to do stuff first.