Переменная объекта не нужна

Конечным параметром является xlUp , а не x1Up.

Версия массива

Option Explicit

Private Sub SplitTourCommand_Click()

    Const cSheet As String = "Splits"

    Dim erow As Long
    Dim vnt As Variant

    ReDim vnt(1 To 1, 1 To 10) As String

    vnt(1, 1) = OriginalTourCode.Text
    vnt(1, 2) = OriginalStartDate.Text
    vnt(1, 3) = OriginalEndDate.Text
    vnt(1, 4) = NewTourCode1.Text
    vnt(1, 5) = NewStartDate1.Text
    vnt(1, 6) = NewEndDate1.Text
    vnt(1, 7) = NewTourCode2.Text
    vnt(1, 8) = NewStartDate2.Text
    vnt(1, 9) = NewEndDate2.Text
    vnt(1, 10) = ReasonForSplit.Text

    With Worksheets(cSheet)
        erow = .Cells(.Rows.Count, 1).End(xlUp).Row + 1
        .Cells(erow, 1).Resize(, 10) = vnt
    End With

End Sub

Версия диапазона

Option Explicit

Private Sub SplitTourCommand_Click()

    Const cSheet As String = "Splits"

    Dim erow As Long

    With Worksheets(cSheet)
        erow = .Cells(.Rows.Count, 1).End(xlUp).Row + 1
        .Cells(erow, 1) = OriginalTourCode.Text
        .Cells(erow, 2) = OriginalStartDate.Text
        .Cells(erow, 3) = OriginalEndDate.Text
        .Cells(erow, 4) = NewTourCode1.Text
        .Cells(erow, 5) = NewStartDate1.Text
        .Cells(erow, 6) = NewEndDate1.Text
        .Cells(erow, 7) = NewTourCode2.Text
        .Cells(erow, 8) = NewStartDate2.Text
        .Cells(erow, 9) = NewEndDate2.Text
        .Cells(erow, 10) = ReasonForSplit.Text
    End With

End Sub