I do not have Acrobat 9 to check but you generally need to have the signing certificate with the private key that signed the signature you want to delete (installed and enabled either in the Windows store or Acrobat Digital IDs) in order to be able to delete this signature.
Open Security Settings dialog, choose Digital IDs and look if you have the signer of the signature. If you do, highlight it, select "Details" and check whether "Details" pane contains private key.
This what happens in Acrobat X and XI. I just presume that the same happens in 9, although I cannot guarantee that.