I also have several old directories which have been getting a handful of link removal requests. I have even had a few threatening demands to remove links or face legal consequences.
But most of the requests seem to be coming from small website owners who have heard something about being penalized for bad links and, to me, seem to be panicking. I charge them $5 and most people pay (some over multiple link directories). I personally think they are doing more damage than good to their websites.
5 Years ago the idea of removing links from a directory for a fee would have been ridiculous, people were just about begging (and paying) for links back then.