A workaround is to define a special css class for this textbox and using it like selector with jQuery
in code aspx code
<asp:Textbox ID=myTextBox" runat="server" CssClass = "AutoCompleteTxtBx" />
in js
$('.AutoCompleteTxtBx').autocomplete('PurchaseHandler.ashx');
In this case, all "duplicated" textbox in your gridview have autocompletion.