I'm exhausted. I'm energetically, emotionally and physically exhausted. I need time and space to recover, but those same requirements hurt people in my life.

I'm a full-time student and work full time. Additionally, a series of family crises over the past half year or so have consumed any free time. I am fucking tired. At the same time, I have a sibling and two friends who are afflicted with borderline personality disorder: I'm not as involved in our relationships when I'm tired and I feel like they're distressed about it.

All three reach out for support (validation, reassurance and perspective) when they're upset. When I'm not there to respond, all three have raised concerns that it's because of something they're doing.

The sibling has a great support system and has made a lot of progress in the last 10 years or so at managing/coping with their symptoms. Sometimes they're mildly annoyed when I can't talk, but appear to quickly get over my unavailability. One of the friends, similarly, appears upset when I say I'm busy or take more than a few minutes to respond to messages. Once I explain that I'm busy, they appear to cool down. This is an about twice-monthly cycle.

I used to give the third friend a level of support that I just can't sustain. They used to reach out to me for support every day, sometimes talking two to six hours each night about perceived conflicts. I explained that when I'm tired and busy I need some space and can't readily be available when they need me. They accept that rationally, objectively, but then explode when I'm not available to talk them down.

TL;DR: I feel burned out. How do I get the time and space I need to help me without hurting them? How do I communicate to my friends and family that my stonewalling stems from my need for preservation and has nothing to do with their behavior?