Nothing is impossible.
won't be active about 10 min (up to their settings)
Ok, the first question here is how would you apply it to user settings? They must be set up under Profile, that requires new profile's field addition
When such field is available and read in bb_cookie.php, another code may dynamically change the following settings (explanations given in Manual
$cookie_expires=900; //15 minutes
$cookie_renew=600; //10 minutes
That will set the cookie to expire in 15 minutes, and if user won't be active within 10 minutes, it should be re-logged in again.
This modification requires the current bug being fixed in miniBB
I didn't tried that all on my side, because it's the question of your custom request, and this is all the information I could provide. Such thing requires a lot of extra coding. Not a simple one for newbies.