As I could not continue to take the risk to have no protection, I decided to reinstall beta2. I turned off User account control, restarted, deleted Windows Live One care beta 2, restarted. I reinstalled Windows Live One Care beta 2 through the set up file that I saved when I downloaded it for the first time I installed beta 2. Nothing came out, no button. Suddenly, I realized it might be a problem at the level of services. I went to Administrative tools, services. The windows Live One Care service was not started. I started it manually and everything went fine. I did not do anything since that time, except turning on user account control and restarting the computer. It worked, the update was installed when I reinstalled Windows Live One Care beta 2! I have the version 2.0318.12. I came in because at a moment in the reinstalling process, it looks for updates.
So, for the moment, it works. I will do the same on my second computer. The problem remains why the service is interrupted and does not restart automatically. At the same time, it stops the security center.
I do not know if it is useful for you. I think that it should be sent as feedback to Windows Live One Care guys.