Pascal,
Going by the numbers of links you're talking about (tens of thousands being only 5-10% of total links) in relation to them being lost in the core update, makes me wonder about their quality. It makes me wonder if your rankings might have dropped, as well--I mean really, except for the people who closely watch the traffic brought in by hard-earned back links, most people would rather not have to worry about the dang things at all. Am I right?
Anyway, the seemingly most obvious explanation is that the pages and/or domains those tens of thousands of links reside on were devalued due to google's algorithm update and Moz's crawler/algorithm didn't incorporate them into subsequent updates as a result. Are you seeing the same sort of thing on other platforms?
It may turn out that the owners of the sites hosting those tens of thousands of links may be able to turn things around on their site(s) and all those thousands of links return to the realm of visibility. But really, I don't know if I'd be clamoring to get them back, if I were you.
If your rankings haven't dropped, consider yourself lucky and take it as a lesson to develop better back links. If rankings have dropped, well, take that as a lesson to get better back links too. : ) In either case, if I were you, I'd take a very, very close look at them with an eye toward disavowing them--and maybe any more thousands you have that you might think could be in jeopardy in a future core-style update.