Google purposefully screws with the links you see. It’s never true. Some good links will never show. I don’t know who is doing your SEO but they should know that.
I have noticed wild fluctuations in the number of links for G&C lately. Suddenly links from posts at forums show up front and good old links from quality sites don’t show.
On the positive side, all the tens of thousands of links from blackhatters have disappeared.
You have old, established sites. Check each link before deleting, and be picky with new ones. Old links are more valuable than new ones. Links to crappy sites drag you down. Go on a case by case basis and clean up. Collect a small number of very good links, hopefully many of them aged. The age of your site gives you a great advantage, don’t ruin it by treating it like a brand new site.