There's a myth that cut or shaved hair grows back stronger, but it is just a myth - cut hair has an angle at its tip which gives the illusion that it is stronger. If hair loss is due to mle pattern baldness, it will go no matter what you do. The advantage of shaving, or cutting it short, is that it looks a lot neater, and shows the world that you don't care, and why should you - no one else does!
Isn't highly illogical to shave your hair to prevent hairloss? Much like my friend who was worried that staring at a monitor all day would lead to him having to wear glasses so bought a pair of antiglare glasses which he wore....!