Apparently windows search uses some sort of modified file properties to 'enhance the search experience'. The references I have read all implicate Live mail in the installation of this enhancement, but it could just as well be a windows update or an Internet explorer update.
The side effect of the enhanced search experience is that any EML files you have saved into the file system from your mail client can't be dealt with as files and nothing you do to move or delete them works. The solution is to change the registry key as shown below. Once that key is set to Zero and you have rebooted you will be able to modify the EML files as normal.