Well, it depends on who did the breaking up.
If the INTP does the dumping, well... it is over and done with. Kaput. And the INTP will get really irked if the dumped person keeps asking around about them or hanging about or pestering them. (They want to avoid the awkward emotions, they want to avoid clinginess, they want to avoid being stalked.)
"When an INTP is dumped? This could be somewhat bad, if the INTP does not really understand why the dumping occurred. At first guess I think this might drive most of any difficulties an INTP might experience in letting go: If they have not been given an explanation and they can't piece one together, then they will obsess over "why it happened" and try to figure it out.
The other reason an INTP might obsess is simply because of the "fascination fixation." INTPs tend to get really absorbed in a particular field, until they learn everything about it they can, and then they drop it and move on. If a human being is the target of this focus, and the person cuts off things before the INTP has learned everything they wanted to know, they still might obsess in finding out all the things they didn't yet know before being able to move on.
Those are just my best guesses right now.