Similar to BearX220, I also throw my BPs into an envelope (which usually tears after several months, so I put the first envelope into a second one, and so on). I begin the process anew at the beginning of each calendar year. Since even thousands of BPs take up little space, and provide potential for future nostalgia (an oxymoron?), I save them in a drawer.

Other than for sentimental reasons, I see no need to keep BPs once the next status year begins (which may be either the beginning of a calendar year, or a membership year). Note that this practice generally maintains BPs beyond the date when miles post because, IME, on occasion status and bonus miles can be deleted from an account - and would then have to be argued with supporting docs - but rarely after the new membership period begins.