You can wrap the <cms:BasicForm /> control with <asp:UpdatePanel/>. Form will be submitted using AJAX call and modal dialog stay open.
You can use javascript to handle end request event which is raised after an asynchronous postback is finished and control has been returned to the browser.
var prm = Sys.WebForms.PageRequestManager.getInstance();
prm.add_endRequest(function (s, e) {
// DO SOMETHING
});