Вам просто нужно, чтобы счетчик даты уменьшился до понедельника-пятницы.
Sub OpenPreviousWorkdayFile()
Const filepath = "\\FileShare\work\"
Dim wb As String
Dim isum As Workbook
Dim dWorkDate As Date
dWorkDate = Date
Do
dWorkDate = dWorkDate - 1
Loop Until Weekday(dWorkDate, vbMonday) < 6 ' Mon=1,Tue=2,etc
wb = "Summary " & Format(dWorkDate, "m.dd") & ".xlsb"
Set isum = Workbooks.Open(filepath & wb)
End Sub