Code breaks down at that line according to debugger. It seems that code wants to cycle through the first file tested over and over again, producing further versions of the same worksheets. It needs to know that it's done its job on the file and should move on.

The main issue seems to be that, rather than just splitting all the worksheets into new files, it also wants to create a new file containing all the worksheets together. If that could be prevented, it is likely the problem may go away.
What does that mean?

Dim n as a Variant. You have been looping thru the code n number of times, but you had used a zero instead of n for the file to open.

couldn't find that issue.

You do realize that this code will also convert the workbook that it is in?

This version works on my machine.
Option Explicit

Function ListFiles()

     ' Subfolder depth: -1 = All subfolders, 0 = No subfolders, 1 or any positive value = maximum depth
     
    Dim dot         As Long
    Dim ext         As String
    Dim n           As Variant
    Dim NewName     As String
    Dim oFile       As Object
    Dim oFiles      As Object
    Dim oFolder     As Variant
    Dim oShell      As Object
    Dim Wkb         As Workbook
    Dim NewBook As Workbook '<<<<<<<<<<<<<<<<<<<<<
    Dim WkbName     As String
    Dim Wks         As Worksheet
    Dim FileFilter As String
    Const FolderPath As Variant = "C:\CSVs\A\"
     
    If oShell Is Nothing Then Set oShell = CreateObject("Shell.Application")
     
    If FileFilter = "" Then FileFilter = "*.*"
     
    Set oFolder = oShell.Namespace(FolderPath)
    If oFolder Is Nothing Then
        MsgBox "The Folder '" & FolderPath & "' Does Not Exist.", vbCritical
        'SearchSubFolders = False
        Exit Function
    End If
     
    Set oFiles = oFolder.Items
     
     ' Return all the files matching the filter.
    oFiles.Filter 64, FileFilter
     
     'Split each workbook's worksheets into new workbooks.
    For n = 0 To oFiles.Count - 1
        WkbName = oFolder.Self.Path & "\" & oFiles.Item(n).Name
        Set Wkb = Workbooks.Open(WkbName, False, True)
        X = Wkb.Name
        dot = InStrRev(Wkb.Name, ".")
        ext = Right(Wkb.Name, Len(Wkb.Name) - dot + 1)
        WkbName = Wkb.Path & "\" & Left(Wkb.Name, dot - 1)
        For Each Wks In Wkb.Worksheets
            NewName = WkbName & "_" & Wks.Name '<-<-<-<-
            Wks.Copy
             'Immediately set a variable the newly created book
            Set NewBook = Workbooks(Workbooks.Count) '<<<<<<<<<<<<<<<<<
            NewBook.SaveAs NewName & "_" & Left(CStr(CDbl(Now)), 10) & ext '<<<<<<<<<<<<<<
            NewBook.Close '<<<<<<<<<<<<<
        Next Wks
        Wkb.Close SaveChanges:=False
    Next n
     
     ' Return subfolders in this folder.
    oFiles.Filter 32, "*"
    If oFiles.Count = 0 Then Exit Function
     
    'If SubfolderDepth <> 0 Then
        'For Each oFolder In oFiles
            'Call ListFiles(oFolder, SubfolderDepth - 1)
        'Next oFolder
    'End If
     
End Function