Once in a while I will drink that last cloudy half bottle right down the day I bottle, just to see the flavor - but it will be flat. They will have a head within a few days, and that's good enough for me, but they do get better for a couple of months at least, If I ever keep one longer than that, I would be qualified to say how long they continue to improve.
By the way, Making (and this is a serious question, not trying to break your chops) - do you speak English as your first language?