More than likely what's happening is a routing issue and not data loss. That error outputs on pages unrelated to file fields. So what I suspect is happening is a Joomla menu issue causing routing problems. Please be sure you have a public and published Joomla menu item to CBs profile page. This menu item doesn't need to be visible, but it still must exist and must be public and published.
The only way a file field can delete a file is if it was explicitly told to from the dropdown, if they uploaded another file, or if they attempted to upload again and the user edit save failed it'll apply a rollback to delete the file. There's no other functionality for deleting files and in short always requires user action.
For testing reference I've an install with file fields filled for over 5 years with no problems. If it's not a routing issue my best guess is some sort of user action triggered the issue or if you've any 3rd party security extensions installed it's possible those deleted the files. How often has this happened?
When you then check under the cb_fields folder under images on the server you find that this user has no folder even though the user did upload the documents.
File fields are stored in the /images/plug_cbfilefield folder. Are you sure you're checking the correct directory?