What Revit Version?
I have never seen a Red X before the name, can you post a screenshot (you can obscure the names)
(When the link can't be found it's red text "not found")
Ps. If the Central File is created (or the local itself, not sure) with the open option "Last Viewed or Editable" then each time opening the model will revert changes to this untill the central (or local) is created.
You can find the option in the pulldown menu of the open button in the Open Dialog box while a workshared model is selected, see:. Specify-Workset-prompt
I Have had user that had the Specify Workset Dialog popup each time the model was opened, after recreating the central model with the option ALL worksets it was gone.
Look at the Workset dialog when the model is opened and see if any workset(s) is closed.