I also had that problem when I upgraded to 4.0.6 and moved the attachments from the File System to the Database and all but four of them worked again.
AdminCP > Attachments > Attachment Storage Type
I would've moved them back from the Database to the File System if my host didn't have the server running on Safe Mode. Too much hassle. So, I can't tell you if reversing that process still allows them to work properly.
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