Mike,

Maybe someone else using Exchange can help. FWIW this code works for me using OE4.01:

* GetAttachment()
if ( this.oleMAPISession.SessionID = 0 )
   return
endif

with this.oleMAPIMessages
   this.mcAttachmentName = ""
   this.mcAttachmentPathName = ""
   this.mnAttachmentType = 0
   if ( this.mnAttachmentIndex < this.mnAttachmentCount - 1 )
      .AttachmentIndex = this.mnAttachmentIndex
      this.mcAttachmentName = .AttachmentName
      this.mcAttachmentPathName = .AttachmentPathName
      this.mnAttachmentType = .AttachmentType
   endif
endwith

return this.mcAttachmentName

* GetNextAttachment()
if ( this.oleMAPISession.SessionID = 0 )
   return
endif

local lcRetVal

if ( this.mnAttachmentIndex < this.mnAttachmentCount - 2 )
   this.mnAttachmentIndex = this.mnAttachmentIndex + 1
   lcRetVal = this.GetAttachment()
else
   lcRetVal = ""
endif

return lcRetVal

Although you only have to make a call to GetAttachment, that action causes all the attachments to be extracted into the sys(2023) folder then you can copy them from there.
>I'm using MSExchange