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This is the belief that is perhaps the strongest in keeping me fighting for the relationship. It is hard to think that love can't carry us through this, if I have faith in it.

I know that is distorted thinking, and a false belief, one of the "ten beliefs that can get you stuck." I don't want to get stuck, but I do want to keep my faith in love.

I think there is nothing wrong with keeping our faith in love. Only, if you believe your partner has a Cluster B disorder (narcissism, borderline, antisocial personality disorder), love alone cannot cure Cluster B. Why do you think love should be able to do that? Why do you perceive it as losing your faith in love because of this? (Not rhetorical questions. But I think many of us cognitively classify behaviours coming from the disorder as healthy but difficult behaviour that can be cured by love, understanding, tolerance etc). And how about your love for yourself? Is it possible to actively maintain both in this relationship?   

Yes I thought and still believe the same thing about love.  I stubbornly stayed in the relationship thinking this.  The bible even says "Love never fails".  One thing to realize though is it takes two to love and make a relationship work.  The realization that I had to come to grips with is that pwBPD can't grasp the concept of love.  Just think of all the things your SO did in your relationship that weren't consistent with love.  Love show's itself in actions.  Whether the SO pwBPD truly meant it when they said it at that instant in time is debatable but love isn't impulsive, you don't love one minute and the next want to end the relationship with no real reason.

So absolutely yes, love can carry two people through anything so keep your faith in love.  It's so sad that pwBPD can never truly love someone and have to go through turmoil their whole lives, can never know peace in loving someone and knowing the feeling of being loved.