"I am trying to run an update query as many times as is necessary for the query to return a statement that there are 0 updates being made."

Make a select query that has the same criteria as the update query, and use a loop something like this, in a standard module:

Function DoTilDone()
    DoCmd.SetWarnings False
    Do While DCount("*","qrySelect")>0
        DoCmd.OpenQuery "qryUpdate"
    DoCmd.SetWarnings True
End Function

Create a macro to "RunCode" for the function.