When someone you care about is pulling away, do you just let them go?

Someone very close to you. Sibling, child, spouse, close friend for many years. When they have decided they just don’t want to spend time with you, do you just let them dissappear? Or, do you try to recapture fun times and get back what used to be there? It seems to me once they have mentally begun to distance themselves it is impossible. Everything you might try backfires and they find fault with everything. And they want to reinforce their decision to pull away. If you let them drift away, then bye bye, the relationship ends also.

I am not really asking for advice, but more what you do in the situation, and how it has worked for you.