This is just my personal experience, but distilled spirits improve as the bottle gets lower, though they all have a tipping point, usually at about the last 100 ml or so of a fifth. As long as you re-cork them, the air can’t circulate and won’t cycle away the ethanol and the phenols and other attached volatiles. I generally take about a year to finish a given bottle, as I don’t drink the same thing over and over. I find the ratio of the spirit’s surface in contact with the air in the bottle matters much more than the time, even over that scale.
A fortified fermentation like vermouth will typically last about two to three months after you open it, but it’s profile will stand up better if you keep it chilled.
Unfortified wine - I personally tend to favor rich fruity and/or full-bodied reds and rosés - will last about two to three weeks as long as it’s re-corked after each opening. I like to pour what I want into my decanter or through my aerator to breathe it, and re-cork the bottle immediately. I do find that re-corking with the wine saver pump slightly improves the longevity and decidedly improves the fullness of the nose and palate over the longevity, but then I like strong aromas and tastes, which is why I’m more of a whiskey and gin guy than a wine guy.
I can’t speak to beer as I rarely drink it.
I will say that palates are very personal and idiosyncratic. Someone who doesn’t think they need something like this tool, probably doesn’t, since they know what they like.
