1.Reopen the modal pop-up again at the end of Postback.
string message = "$('#myModal').modal({ backdrop: 'static', keyboard: false, show: true });";
Page.ClientScript.RegisterStartupScript(this.GetType(), "CallMyFunction", message, true);
2.You can call show() method during postback to prevent the modal popup window from closing
$("#myModal").modal('show');