Still the same problem for me and new “large descriptions” do not appear in database.
I figured out more details concerning my problems with long descriptions: old texts are still there, but since the last update the plug-in does not write in wp_links_extrainfo. There is no data set for new links. If I create an entry in wp_links_extrainfo it works fine. I can change the long description and it appears on the listing page, but for new links it does not create an entry. Maybe that is helpful for you. Now I will find out, why it does not write to wp_links_extrainfo with first submission of a link.
Maybe I get a solution on link library, before I solve it myself.
I think that the information is in the database but when you try to edit the link, it will be gone.
I guess it is a bug
@glehrer
On the WP-site where I had troubles, I saved the settings and content of the table wp_links_extrainfo, than I deleted the tabel and installed link library new. Now it works also there.
Please try upgrading to version 4.7.4. It should resolve the issue.
