Sometimes Mptag doesn't show correct 'cover varies' message

Easily.
As tag data is mapped to the internal representation of tag fields (and there can only be one) depening on the settings in File>Options>Tags>Mpeg you would probably end up with the contents of ID3V2.x tags to be displayed.

Even though you explained at length what you do, it hardly answers any of the questions to narrow down the cause of your initial claim:
What was different with the 140th file which had a cover but did not show it?
Do you have the files locally?
Do other programs access the files at the same time (so that reading the tags gets delayed)?
Which types of files are these?
Did you check the files for integrity with the known tools ?