Change to multiple worksheets in same file?

Try this code - The sorting code was wrongly placed and that could be causing issues -

Option Explicit

Sub make_changes()

Dim Master As Workbook
Dim sourceBook As Workbook
Dim sourceData As Worksheet
Dim CurrentFileName As String
Dim myPath As String
Dim lrow As Long, i As Long

'The folder containing the files to be recap'd
myPath = "D:\Test"

'Finds the name of the first file of type .xls in the current directory
CurrentFileName = Dir(myPath & "\*.xls")

'Create a workbook for the recap report
Set Master = ThisWorkbook

Do
    Workbooks.Open (myPath & "\" & CurrentFileName)
    Set sourceBook = Workbooks(CurrentFileName)
    Set sourceData = sourceBook.Worksheets("Database")
    
        With sourceData
            lrow = Master.Worksheets("Database").Range("A" & Rows.Count).End(xlUp).Row
            For i = 2 To lrow
                .Columns(1).Replace Master.Worksheets("Database").Range("A" & i).Value, Master.Worksheets("Database").Range("B" & i).Value, xlWhole
                If Master.Worksheets("Database").Range("C" & i).Value <> "" Then .Range("A" & .Rows.Count).End(xlUp).Offset(1, 0).Value = Master.Worksheets("Database").Range("C" & i).Value
            Next i
            .Cells.Sort Key1:=Range("A2"), Order1:=xlAscending, Header:=xlYes, OrderCustom:=1, MatchCase:= _
                False, Orientation:=xlTopToBottom, DataOption1:=xlSortNormal
        End With
       
    sourceBook.Close
  
'Calling DIR w/o argument finds the next .xlsx file within the current directory.
CurrentFileName = Dir()
Loop While CurrentFileName <> ""

End Sub