Give this a shot, if the coloring of the date cells was just for emphasis and not needed,
remove the variable from the declarations and the two color lines in the macro.
Code:
Sub rsrasc()
Dim i As Long, ws As Worksheet
Dim rng As Range, cel As Range
Dim lr As Long, dte As Date, colour As String
Application.ScreenUpdating = False
Application.Calculation = xlCalculationManual
For i = 1 To Sheets.Count
With Sheets(i)
dte = .Range("A4").Value
colour = .Range("A4").Interior.Color
lr = .Range("B" & .Rows.Count).End(xlUp).Row
For Each cel In .Range("C6:C" & lr)
If cel.Offset(, -1) <> "" Then
With cel
.NumberFormat = "d-mmm-yy"
.Interior.Color = colour
.Value = dte
End With
End If
Next cel
End With
Next i
Application.Calculation = xlCalculationAutomatic
Application.ScreenUpdating = True
End Sub