Thank you DumDum. I'm sorry I didn't remember that it was you who published the solution. I always had this step in mind as a possible last resort, and I was hoping I wouldn't have to apply it. I trusted Microsoft to solve it but time was passing by and I decided to go for it.
I also noticed the glitch when launching a game, but it reconnected in a second without doing anything until, after an hour or so, I've got a low battery warning. I had to plug the cable because the controller was unmanageable.
Tomorrow I will try with a previous "play and charge" kit's battery and see if it happens again. Also, I have a tester and I will check the "old" batteries' condition. I will keep you informed.
I get same glitch sometimes launching games, i make sure the xbox controller is turned on before the game is launched or i think sometimes on some games. I started the controller on the game menu, power on the controller then starting tapping button on moving the joystick to try to make it work after a few seconds it works. If that does not work i restart the game.
I don't know maybe the more you use on games on bluetooth it works out too be more reliable or something? After that you will no longer need to plug it through the cable unless there is a new firmware update with major fixes.
I ignore the battery level low message because i think that is a glitch too, i am able to carry on playing games.