Hi heartbreaksandearthquakes,
it is important to think about abandonment and avoid triggering it. Absolutely!
But you know what - we can't avoid triggering the pwBPD. Living focused on avoiding the triggering is avoiding living. It is walking on egg-shells. Not a real alternative. We may choose to baby someone for a short time - that is ok - but it is not a way of life.
So worrying about it is good. Then we know when we trigger abandonment when life or our dear pwBPD forces our hand. So we can do our best to manage the fallout e.g. trying to minimize the trigger by doing a limited timeout or sufficiently validate abandonment where possible.
Navigating the tension between our very valid self interests and the needs of the pwBPD is a balancing act. Plotting the course and steering your way through it is not simple. Describing concrete situations and interactions and asking questions is a good way to get the best out of the board

Today, his mood changed from intensely cheerful to unkind and combative over the course of an hour. I tried to remain positive and supportive, but nothing that I tried to do could pull him out of this episode. He frequently says that he knows that I will break up with him, even up to several times a day when he has what I like to think of as a "borderline" day. He also likes to insist that "I hate him." I don't know what to do in these situations other than tell him "I don't hate you. I love you" or saying "I'm not going to break up with you. Why do you think that?" I never know what more I can do in these situations. Am I wrong to leave his house for the night in these situations, even if I don't have plans? I feel odd repeating my love/devotion to him 10+ times as he responds with "you hate me" or "you're going to break up with me." I just feel that I've stayed before but I become miserable trying to convince him of something that apparently I am not able to convince him of. If I leave in a situation like this, after expending all of my effort, is it abandonment? Does the person with BPD view it as abandonment?
Good intentions but please read up on
invalidation (see the post LESSONS at the top). Being positive around a depressed pwBPD is going to invalidate the person and make matters worse. The way you communicate here really matters and you can help him a lot by modifying your approach.