object permanence, or the concept of "out of sight, out of mind", is not, i dont think, literally meant to suggest that our partners "forget we exist" when we arent in front of them. the title of this thread, and most of our own experiences would reasonably lead us to believe to the contrary.
object permanence is really the ability to self soothe feelings of loneliness, emptiness, abandonment, etc, with images of, with the sense of, and the comfort of, loved ones, our memories of them, the things we look forward to with them. to know that we are loved, and to feel that love.
i remember the many nights, when i wasnt with my ex, that she would sink into total despair, and shed ask to speak to me on the phone. her feelings of loneliness were palpable and i never understood it. id remind her of my love for her, try to cheer her up. remind her of things she had to look forward to. im sure that she appreciated the effort, but for the life of her, it made no difference in that moment. i could sense that when we were getting off the phone, she was going off to cry.
this impaired ability (to varying degrees) can speak to a lot of aspects of BPD.
when we are talking about how quickly some of our partners seem to move on though, a hard thing for me to swallow was that my ex had, perhaps not completely, but on a lot of levels, grieved the relationship. it wasnt just hard to swallow though, it was hard to see, given that it hadnt even been long since she expressed "falling in love with me all over again". but people with BPD traits over express themselves (for better and worse), and if your ex was unsure about breaking up, maybe having second thoughts, all of that can make for a very confusing breakup.
Yes, that's well explained. The water bucket with holes in it is a good metaphor. It's like they have a problem instantiating positive human interactions, it's never enough to be shown or told that someone cares for them. They have to fish for these compliments any time they're 'thirsty' for emotional supply.
You also make a good point about the ex being unsure. Something I myself have been guilty of since the breakup is seeing her behaviour in binary terms, assuming their actions were total and without any regret. I'll explain it all tomorrow, but in my case, I think my ex literally decided to breakup with me while she was drinking at the bar immediately before meeting me for what would be our last date...