Why does No Contact lead to successes in spite of a lack of object constancy?
Like you said, that person left feeling engulfed and you made the mistake of reaching out too frequently. It smothered them and they had to "escape". We all do that when these relationships get difficult, so don't feel like you're alone. It's intuitive to fight for the relationship.
With BPD though, the person has to have time to sort of find themselves and figure out what matters in their life. That takes time and it's not a guarantee of relationship success...but it does give everyone time to heal and see things more objectively.
You maintaining no contact allows you to heal and focus on your own mental health, which has taken a hit going through all of this. Again, the healing and gaining more mental clarity is the success part, which is why you'll see advice to stay busy with favorite hobbies and friends/family. Sitting around waiting for the phone to ring is hurting you...moving on and adjusting to a life without your ex is healthy because it breaks the co-dependency.
In time, both of you should become better people...although your ex will still have a major mental illness. With no contact, you can hope that the ex reaches out from genuinely missing you and by that point, you'll have healed enough to see the possibility of the relationship with fresh eyes. There's no guarantees here that the relationship will succeed, which is why you must focus on yourself and actually healing from what was broken. That way you walk away a winner no matter what.
One other trait of BPD is recycling relationships through different stages, and probably around half of the members here have seen their ex's want to rekindle the relationship. So there's definitely still hope if you can avoid repeating past mistakes.
Under the tools section at the top of this page, there's some great lessons on better communication techniques that will help you prepare. Study them and take it to heart, because you're the one who will have to make the initial changes. Good luck!