One acquaintance has ~500K books in their library. A mix of public domain and corporate documents. So far, they have had no issues with books/covers disappearing so I would say that it is not an issue with library size.
The first question that comes to mind is where your library is being stored. If it is not on local media, that is the most likely explanation for your issue. See
I am getting errors with my calibre library on a networked drive/NAS? in the calibre FAQs.
As for checking for books with no cover, you can use the Quality Check plugin's Check Covers option with No cover selected.