Eventually you get dirty looks. The key is before the flight takes off when they ask if you'd like a drink ask for (in my case) "2 jacks and a coke" and be charming. Then when they come around ask for "the same." Then you only have to be the annoying guy who clicks the button for the flight attendant once and say "you know I hate to bother you but is there any chance I can get another of the same before we land? I will drink it fast
(because sometimes they shut you down with they're gonna land soon so they can't).
So I would estimate on a 50 min flight you got 6.
*Source: Alcoholic who flies a lot