I have read several posts where the complaint of wasted wine used in a recipe came up. I was surprised as wine has an amazing shelf life and even "soured" can be used to cook and even can. If you don't drink much; wine freezes well for recipe use, that way you don't have the concern of souring, better yet don't use wine experiment with herbs or mustard even vinegar's.
The best tip is to never cook with something you would not normally eat/drink. Seems obvious but as an educator I oft times find that when people "hate" a food that is gospel and no perfect preparation will change their mind.
Actually I find that is not true.
Vermouth is wine and once open oxidizes and the flavor deteriorates.It should definitely be refrigerated after opening to slow the down hill slide.
Many say that since it is fortified that it is shelf stable but it is typically 18% but that is relatively low.
Many CA Zins and Syrahs are about the same and you wouldn't leave a open bottle stored for months on end and expect it to taste good.
There are a range of opinions out there about it but most Cocktail enthusiasts (both mixers and drinkers) agree that it should be refrigerated after opening and consumed in a month or so.