Some Questions:
What are your rule settings that run this?
Are you manually running the rule on the folder, or is the rule automatically running on a trigger?
Are you getting any error messages?
Try the following:
Make sure the rule that runs your autoforward macro is lower on the rule list than the rule that files messages in that subfolder (if you're using one).
Also, since I don't know what triggers your macro, exactly, it's possible it is stopping when it is encountering a non MailItem object. Try this change:
Sub ChangeSubjectForward(olObj As Object)
dim Item As Outlook.MailItem
If olObj.Class <> olMail Then 'Making sure it is an email message
msgbox("Object Was Not MailItem")
Exit Sub
End If
Set Item = olObj
Item.Subject = "TAG NUMBER1234" & Item.Subject
Item.Save
Set myForward = Item.Forward
myForward.Recipients.Add "Email@email.com"
myForward.Send
End Sub
If you keep getting the message "Object Was Not MailItem" then the wrong objects are getting passed to your sub.