VBA - Count Values within a certain Date Range

Formula Solution
Although I acknowledge that you are looking for a VBA solution to this (perhapse for a good reason), I want to point out that you can solve this by using formulas. You could get the result you are looking for by using an array formula like:

{=IF(SUM(IF(FREQUENCY(($A$2:$A$13=A2)*(MONTH($B$2:$B$13)),($A$2:$A$13=A2)*(MONTH($B$2:$B$13)))>0,1))>3,"Selected","")}

This will return Selected if the color is found in at least three different months.

To use this, type the formula in cell C2, commit by pressing CTRL+SHIFT+ENTER (since it is an array formula) and drag the formula down along side of your data.

VBA+Formula Solution
As you commented that you need this applied in a generated report, you could simply use VBA to type the formula into the sheet:

Sub AddFormula()
    Dim MstrSht As Worksheet
    Dim ColorRng As Range
    Dim DateRng As Range
    Dim i As Integer

    Set MstrSht = ThisWorkbook.Sheets("masterfile")

    'Set Color Range and Date Range
    Set ColorRng = MstrSht.Range("A2:A" & MstrSht.Cells(Rows.Count, 1).End(xlUp).Row)
    Set DateRng = MstrSht.Range("B2:B" & MstrSht.Cells(Rows.Count, 1).End(xlUp).Row)

    'Add Formula to cells in column C
    For i = 2 To MstrSht.Cells(Rows.Count, 1).End(xlUp).Row
        MstrSht.Cells(i, 3).FormulaArray = "=IF(SUM(IF(FREQUENCY((" & ColorRng.Address & "=A" & i & " )*(MONTH(" & DateRng.Address & ")),(" & _
            ColorRng.Address & "=A" & i & ")*(MONTH(" & DateRng.Address & ")))>0,1))>3,""Selected"","""")"
    Next i
End Sub

VBA-Only Solution
While completely disregarding your original code, you may be able to get inspired by this take on a VBA-only solution

Sub MarkColors()
    Dim MstrSht As Worksheet
    Dim DataArr As Variant
    Dim ColorArr As Variant
    Dim MonthCol As Collection
    Dim CloseToDate As Date
    Dim MaxDate As Date
    Dim c As Long
    Dim i As Long

    Set MstrSht = ThisWorkbook.Sheets("masterfile")

    'Define date
    CloseToDate = DateSerial(2016, 6, 6) '<~~ Define date

    'Load Data into Array
    DataArr = MstrSht.Range("A2:C" & MstrSht.Cells(Rows.Count, 1).End(xlUp).Row)

    'Find distinct colors
    ColorArr = ReturnDistinct(MstrSht.Range("A2:A" & MstrSht.Cells(Rows.Count, 1).End(xlUp).Row))

    'Remove any values in the arrays third column
    For i = LBound(DataArr, 1) To UBound(DataArr, 1)
        DataArr(i, 3) = ""
    Next i

    'Loop Each Color
    For c = LBound(ColorArr) To UBound(ColorArr)
        Set MonthCol = New Collection
        MaxDate = 0
        For i = LBound(DataArr, 1) To UBound(DataArr, 1)
            If DataArr(i, 1) = ColorArr(c) Then
                'Load the colors months into a collection
                On Error Resume Next
                MonthCol.Add Month(DataArr(i, 2)), CStr(Month(DataArr(i, 2)))
                On Error GoTo 0
                'Find Max Date
                If DataArr(i, 2) <= CloseToDate Then
                    MaxDate = Application.WorksheetFunction.Max(MaxDate, DataArr(i, 2))
                End If
            End If
        Next i

        'If the color were found in three or more seperate months then the row with date closest to CloseToDate gets flagged
        If MonthCol.Count > 2 Then
            For i = LBound(DataArr, 1) To UBound(DataArr, 1)
                If DataArr(i, 1) = ColorArr(c) And DataArr(i, 2) = MaxDate Then
                    DataArr(i, 3) = "Selected"
                End If
            Next i
        End If
    Next c

    'Print results to sheet
    MstrSht.Range("A2:C" & MstrSht.Cells(Rows.Count, 1).End(xlUp).Row) = DataArr
End Sub

'Return Array With Distinct Values
Function ReturnDistinct(InpRng As Range) As Variant
    Dim Cell As Range
    Dim i As Integer
    Dim DistCol As New Collection
    Dim DistArr()

    'Add all values to collection
    For Each Cell In InpRng
        On Error Resume Next
        DistCol.Add Cell.Value, CStr(Cell.Value)
        On Error GoTo 0
    Next Cell

    'Write collection to array
    ReDim DistArr(1 To DistCol.Count)
    For i = 1 To DistCol.Count Step 1
        DistArr(i) = DistCol.Item(i)
    Next i

    ReturnDistinct = DistArr
End Function

Note, that I am unsure about exactly which date you want to be the "selected" date. Thus, I have added the variable CloseToDate, and the code will "select" the row with the date that is closest (but smaller) than this particular date.