Try this, i had a look at your workbook but don't know what i am supposed to be doing with it or how to operate it....that said you have other problems in your code(s) where you have Dot qualifiers that you do not need, anway try this one as i added .name to xlLastRow(Sheet).
[VBA]
Private Sub cmdEmpAdd_Click()
Dim Sheet As Worksheet
Dim strLastRow As Integer
For Each Sheet In Sheets(Array("Master", "Leave Request"))
With Sheet
'Get last row
strLastRow = xlLastRow(Sheet.Name)
Application.EnableEvents = False

'If textboxes not null then fill data of textboxes to worksheet.
If (frmEmpRequest.cboEmpName.Value <> vbNullString And frmEmpRequest.cboEmpType.Value <> vbNullString And _
frmEmpRequest.txtEmpStart.Value <> vbNullString And frmEmpRequest.txtEmpEnd.Value <> vbNullString) Then

.Cells(strLastRow + 1, 1).Value = frmEmpRequest.cboEmpName.Value
.Cells(strLastRow + 1, 2).Value = Format(Now, "mmm-dd-yyyy hh:mm:ss")
.Cells(strLastRow + 1, 3).Value = frmEmpRequest.cboEmpType.Value
.Cells(strLastRow + 1, 4).Value = CDate(frmEmpRequest.txtEmpStart.Text)
.Cells(strLastRow + 1, 5).Value = CDate(frmEmpRequest.txtEmpEnd.Text)
strLastRow = strLastRow + 1

'Update listbox with added values
frmEmpRequest.lstEmpBox.RowSource = "'Leave Request'!A2:E" & strLastRow
Else

MsgBox "Please Enter Data"
End If
End With
Next Sheet
'Empty textboxes
frmEmpRequest.cboEmpName.Value = vbNullString
frmEmpRequest.cboEmpType.Value = vbNullString
frmEmpRequest.txtEmpStart.Value = vbNullString
frmEmpRequest.txtEmpEnd.Value = vbNullString

Application.EnableEvents = True

End Sub
[/VBA]