msgInternal.Delete is deleting the open message from Outlook. The following version will remove the temporary file also.

Based on skattoni's process for handling attached messages, the following should print the PDFs, though what you mean by 'copy' them I am not sure. It saves them in the named folder. The code does not include any error handling for PDFs of the same name:

Option Explicit
Sub PrintPDFs()
Dim olFolder As Folder
Dim olItem As MailItem
    Set olFolder = Application.Session.PickFolder
    For Each olItem In olFolder.Items
        msgAsAttachment olItem
    Next olItem
lbl_Exit:
    Set olFolder = Nothing
    Set olItem = Nothing
    Exit Sub
End Sub

Sub msgAsAttachment(olItem As MailItem)
Dim att As Attachment
Dim sFname As String, sIntFname As String
Dim sExt As String
Dim msgInternal As MailItem
Dim attInternal As Attachment
Const pdfApp As String = "C:\Program Files (x86)\Adobe\Reader 11.0\Reader\AcroRd32.exe"
Const tempFileName As String = "dummy.msg"
Const tempFolder As String = "C:\Test\"
    For Each att In olItem.Attachments
        sFname = att.FileName
        sExt = Mid(sFname, InStrRev(sFname, Chr(46)))
        Select Case sExt
            Case ".msg"
                att.SaveAsFile tempFolder & tempFileName
                Set msgInternal = CreateItemFromTemplate(tempFolder & tempFileName)
                For Each attInternal In msgInternal.Attachments
                    sIntFname = attInternal.FileName
                    sExt = Mid(sIntFname, InStrRev(sIntFname, Chr(46)))
                    If sExt = ".pdf" Then
                        att.SaveAsFile tempFolder & sIntFname
                        Shell pdfApp & " /n /h /t " & tempFolder & sIntFname
                    End If
                Next
                msgInternal.Delete
                Kill tempFolder & tempFileName
            Case ".pdf"
                att.SaveAsFile tempFolder & sFname
                Shell pdfApp & " /n /h /t " & tempFolder & sFname
        End Select
    Next
lbl_Exit:
    Set msgInternal = Nothing
    Exit Sub
End Sub