Hi @Raffaele1972,
the need to validate the browser each time it is used depends essentially on the fact that part of the recognition is saved on the browser itself.Now, very few things can be saved on the browser: cookies and data in session storage. TeamViewer makes use of the first to store a part of the recognition and if the user's polices provides for the cancellation of browser navigation data at each session close, you will lose what you have stored and experience the behavior that you described yourself.
There is a long discussion on the volatility of the system chosen by TeamViewer to implement the device recognition, but it does not seem to have changed much recently.
So you should check the options of your browser to understand if a data cancellation is really expected every time it is closed; having established this presence, you should consider whether or not it is possible to keep the cache.
Regards.