Try...

Sub Update()
Application.ScreenUpdating = False
Application.DisplayStatusBar = True
Application.StatusBar = "Please wait while updating..."
Application.Wait Now + TimeValue("00:00:02")
On Error GoTo endo
Sheets("Web").Select
Range("A40").Select
Selection.QueryTable.Refresh BackgroundQuery:=False
Sheets("TOP").Select
Application.StatusBar = False

Exit sub

endo: MsgBox "Please relogin the web"
End Sub

And don't forget to reset the error  catching before getting out of the
routine.

On Error GoTo 0
Exit Sub

Error handling is a touchy subject for a lot of people.

I tend to try and handle stuff "inline" as it were, and I use a variable to
catch the error number so that I can reset the handler immediately.

Public lgErrNum as long

Sub Update()

Application.ScreenUpdating = False
Application.DisplayStatusBar = True
Application.StatusBar = "Please wait while updating..."
Application.Wait Now + TimeValue("00:00:02")

On Error Resume next
Sheets("Web").Select
lgErrNum = Err.Number
On Error GoTo 0
Select case lgErrNum
Case 0
Case Else
Application.ScreenUpdating = True
Application.DisplayStatusBar = False
MsgBox "Please relogin the web"
Exit Sub
End Select

Range("A40").Select
Selection.QueryTable.Refresh BackgroundQuery:=False
Sheets("TOP").Select
Application.StatusBar = False

End Sub

Or....

On Error Resume next
Sheets("Web").Select
lgErrNum = Err.Number
On Error GoTo 0
Select case lgErrNum
Case 0
Range("A40").Select
Selection.QueryTable.Refresh BackgroundQuery:=False
Sheets("TOP").Select
case else
MsgBox "Please relogin the web"
End Select

Application.ScreenUpdating = True
Application.DisplayStatusBar = False



I's more coding I know but each error is dealt with there and then and it
becomes pretty standard. Also each error condition can be dealt with in the
select statement.

The message  box is the next line after Application.StatusBar = False, so
there is nothing to stop it being executed. Put in an Exit Sub after the
last line you want to execute.