There comes a time in everyone's life when they must decide if a relationship is worth fighting for. In this case, I'm not referring to romantic relationships, but friendships.
When a friendship gets to the point where the other person has stopped showing the same amount of care, when they have clearly stopped fighting for your relationship, it's best to reciprocate by doing the same.
Like a romantic relationship, friendships can get to a toxic point over time (regardless of how strong your relationship is/was).
There's a common misconception that people believe they should not break up with someone without a valid reason. In other words, if the state of your friendship isn't severe then why cut ties.
I don't know about you, but if I have a friend who shows no signs of interest or the slightest bit of care for me, then I wouldn't want to continue sitting around pondering the state of our relationship when they've made it clear.
If I cut ties with someone I was once close to, I do reassure them that no matter what, I'll always be there if they truly needed me. However, I refuse to stay friends just to wait around until it's most convenient for them to see and/or speak with me.
As we grow older we have more responsibilities—aka adulting—but a genuine person will always find time for those most important to them. Time doesn't necessarily have to imply meeting in person; a mere phone call to check in will suffice.
Don't allow yourself to stay friends with someone purely because you have history. Growing close and drifting apart is a natural part of life.