The button is being hidden but your button click is causing a postback which is causing the whole page to be refreshed which is putting the button back. Change the visibility of the button in your BtnSubmit_Click event in code-behind;
BtnSubmit.Visible = false;
It could also be that the ID you are using is wrong, asp.net changes the IDs of items when they are rendered to the client.
$("#<%=BtnSubmit.ClientID%>").click(function () {
$("#<%=BtnSubmit.ClientID%>").hide();