The session is dropped many times with SSL ON

If you use the Support Panel console with the SSL option ON and the session is dropped many times maybe this happen because a SSL session demand a lot resources in the connection from your hosting.

In some standard hosting is very difficult to use the SSL option ON, in a dedicated or VPS you should not have this issue.

If your site support http and https and bouth point to the same location you can use the support panel without SSL.

Try to can change the server info for a regular http domain and disable the SSL option, the support panel should be work smooth.