At first I tough that the issue could be PHP permissions because Chevereto checks the existence of each homepage cover and when it fails to do that it reverts the database setting, so it avoids doing an re-check on every successive homepage load.
Then you mentioned that you also are missing some images so that's tells me that it is a rollback because if Chevereto (PHP) isn't able to read the image, it shows an image replacement because the record is still in the table.
So if you can confirm that the images aren't not being even listed then the issue is a rollback. If you see a grey block with an icon of two images (not found replacement) then the issue is PHP permissions.
In any case, this is most likely a server issue anyway and is not new that your host says opposite. I mean, it happens only to you how it won't be a server issue?
Hope it helps.