How do i maintain the SSL connection between client and the F5 after login to a web page

ensure you have two virtual servers setup on the LTM. The first listening on your preferred https and the second on http. You then need to attached the pre-packaged f5 irule for http-to-https redirect "_sys_https_redirect" to the virtual server listening on http. This has always worked and redirects to the virtual server listening on https.