Hello Robert, It sounds like the foil screen might have been damaged and is causing poor shaving performance. Typically, a screen will get small holes or tears in it after providing good service for some years, however, these very thin screen foils, can get damaged other ways too.
The best way to restore the best shaving performance is to replace both the foil screen AND the cutter head block (cutter head) as it could be possible that the cutter blades have become damaged or nicked and have caused the foil screen to become damaged, as a result.
I would contact www.electricshaver.com
and see if you can purchase a new set of the cutter block head and the screen foil for your particular Braun shaver model. As the Braun 360 is a tradename used on a couple of different model numbers, you really need the four (4) digit model number in order to locate the correct replacement parts.
Here's a link to their page with the various Braun replacement cutter blocks and foil screens. You might find your model number amoung them, otherwise, you can also give them a call at 1-888-476-1785 and ask them to assist you with selecting the proper replacement parts.
As you are no doubt aware, replacing the cutter head and foil screen is the best and simplest way to restore an electric shaver to a like new shaving condition and much less expensive than replacing the entire shaver.
I hope you find this Very Helpful and best regards!