The fact that you are saving the documents as PDF format may have something to do with it.
Try the following instead. I don't think you can dismiss the conversion prompt in VBA. You can dismiss it from the message itself.
Code:
Option Explicit
Sub UpdateDocuments()
Application.ScreenUpdating = False
Dim strFolder As String, strFile As String, wdDoc As Document
Dim strDocName As String
strFolder = GetFolder
If strFolder = "" Then Exit Sub
strFile = Dir$(strFolder & "\*.pdf")
While strFile <> ""
Set wdDoc = Documents.Open(FileName:=strFolder & "\" & strFile, AddToRecentFiles:=False, Visible:=False)
strDocName = Replace(strFile, ".pdf", ".docx")
wdDoc.SaveAs2 FileName:=strFolder & "\" & strDocName, FileFormat:=wdFormatXMLDocument, AddToRecentFiles:=False
wdDoc.Close SaveChanges:=wdDoNotSaveChanges
strFile = Dir$()
Wend
Set wdDoc = Nothing
Application.ScreenUpdating = True
End Sub