I think its also very dependent on whether the person going through the MH episode appears to be doing what is in their control to tackle it.
This may be very very unfair. But what often makes people who are caring/supporting people in these situations crack is the repetition and the lack of willingness to learn from the mistakes. If you watch someone constantly indulge in destructive or self-destructive behaviour, get support, get help and then go back into a cycle of rinse and repeat there is a compassion fatigue which eventually kicks in.
When my husband was at the peak of his crisis he was constantly threatening suicide and would send me frightening video clips of himself doing things which were meant to imply that he was about to kill himself. Or strings of texts, repeated phonecalls saying he was suicidal etc. It always felt like these were timed for maximum disturbance/inconvenience: always when he knew I was putting our daughter to bed or he knew I was at work or at 3am. This would often happen about once a week.
Most people can tolerate a few episodes of this and be "there" for someone because they realise the person is in distress and not in their right mind. But when the person receives help, medication, counselling and the episodes continue to happen once a fortnight, once a month etc there's a point where it starts to feel quite manipulative.
Again, I think some people probably keep their mental health issues to themselves more (and I'm not sure that's necessarily great either). So this won't apply to everyone.
But I think what is frustrating to the friends in supporting roles is that often people appear not to be willing or able to break the cycles of these difficult behaviours, they seem almost to become a crutch. Although you understand in theory that its not someone's "fault" you do eventually become cynical and resentful when yet another disturbing and chaotic incident forces you to abandon the things you need to do for yourself.
This is why professional support is so important and of course there's very little of that available at the moment so it's a Catch 22. But I do think presenting the appearance of trying to tackle the situation rather than appearing to just accept that this is the status quo goes quite a long way in convincing friends to stick around.