How long does it take before the taste 'flies away' It is said that the taste 'flies away' from an opened beer, and if the bottle is left open too long, it doesn't taste good next day.

Has it actually been measured how long it takes before the taste 'flies away'?
I would say that it has to do more with carbonation than anything else. Like soda, beer goes flat after a while and tastes bad (or not as good) when the carbonation is gone. Some beers have more carbonation than others, so I don't think you can accurately measure this, it really depends on the brew.

Oxidation (exposure to air) also may negatively impact the flavor. Of course, I wouldn't recommend exposing a beer to air for weeks and then drinking it due to various health concerns and I can't say I've ever tried it, nor do I want to.