Whoops! That should be:
It still stops in the middle of the file!

Sub FastAcNos()
Dim objFSO As Object
Dim objFolder As Object
Dim objFile As Object
Dim AcNo As String
Dim eAc As Long
Dim i As Long
Dim sh As Long
Dim fndAc As Range
Dim tbox As TextBox

On Error GoTo Errorhandler
Application.ScreenUpdating = False
eAc = Sheets("Sheet1").Cells(Rows.Count, 1).End(xlUp).Row

Set objFSO = CreateObject("Scripting.FileSystemObject")
Set objFolder = objFSO.GetFolder("c:\Documents and Settings" & _
"\zzfy98\My Documents\Test") 'change directory

For Each objFile In objFolder.Files
If objFile.Type = "Microsoft Excel Worksheet" Then
Workbooks.Open Filename:=objFolder.Path _
& "\" & objFile.Name, UpdateLinks:=False

With Workbooks(objFile.Name)
For sh = 1 To .Sheets.Count
bDone = True
For i = 1 To eAc
If LCase(ThisWorkbook.Sheets("Sheet1") _
.Cells(i, 2).Value) < "yes" Then
' All accounts not found
bDone = False

AcNo = ThisWorkbook.Sheets("Sheet1").Cells(i, 1).Value
With .Sheets(sh).Cells

Set fndAc = .Find(AcNo _
, LookIn:=xlValues _
, Lookat:=xlPart _
, MatchCase:=True)
End With

If Not fndAc Is Nothing Then
ThisWorkbook.Sheets("Sheet1"). _
Cells(i, 2).Value = "Yes"
Else
' Tom's Code:
For Each tbox In .Sheets(sh).TextBoxes
If InStr(1, AcNo, tbox.Text, vbTextCompare) Then
' AcNo found
ThisWorkbook.Sheets("Sheet1").Cells(i, 2).Value = "Yes" ' I
assume???
End If
Next tbox

End If

End If
Next i
If bDone Then
.Close False
Exit Sub
End If
Next sh
.Close False
Set objFile = Nothing
End With
End If
Next

For i = 1 To eAc
With ThisWorkbook.Sheets("sheet1")
If IsEmpty(.Cells(i, 2)) Then
.Cells(i, 2).Value = "No"
End If
End With
Next
Errorhandler:
Application.ScreenUpdating = True
Set objFSO = Nothing
Set objFolder = Nothing
Set objFile = Nothing
End Sub