OK, these questions are for just the really smart guys

I'm fixin' my coffee this mornin' and these questions start to bug me. So I thought I'd share.
I like my morning coffee. Sometimes black. Usually with half and half. The half and half has a long self life. Much longer than milk.
Why would it last longer?
The half and half has a "shake well" instruction on the carton. It doesn't say "shake well before use" and it doesn't say "shake well often" and it doesn't say "shake well every time you pick up the carton".
How often is shaking is needed? Once? Every time? (I know, first world problem.)
I'm sure there's some settling of the contents but, how often you would need to shake would depend on how fast it settles, right? I hate vague instructions. Kind of like "salt to taste", which in my case usually means "salt until you realize you've added too much salt".