The "Keep me logged in" option is built into the template. Since this option is hard coded into the eCommerce store, there is no configuration to disable/enable this link when editing the store in Luminate Online. It may be possible to hide with the use of HTML/CSS/Javascript.  Support is not able to assist with developing or the deployment of custom code. If you would like to pursue the route of engaging Professional Services for a project to develop the custom code or to modify the template then contact support  so they can submit the request.