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

This has to be due to a redirect or link on the web page as the HTTP connection is established from the client side.

If you do not need to connect to the server at all using HTTP then assign the default HTTP to HTTPS redirect iRule (_sys_https_redirect) on the HTTP Virtual Server, this will redirect all HTTP request to the HTTPS Virtual Server.

You can also track the connection using Google Chrome and the Inspect feature, right click on the page select Inspect from the menu. In the Developer Tools window select Network and tick Preserve log option and start.

Go to login page and login to track the journey, expect you to see the change from HTTPS to HTTP as a Redirect (status code 301 or 302) or as a simple new connection from a link, maybe the POST of the login form.