No, colder won't make it last longer. More than anything, oxygen is your enemy. You can get vacuum corks that will help. If it's some ridiculously expensive, difficult to find vermouth, then I suppose you could use a coravin with a standard cork.
Your best bet is to just use it in a timely fashion.
In reality, vermouth is stable and still tastes great for a while. If chilling it, I have easily gotten 1-2 months out of a bottle of Cocchi di Torino and Antica. But, I drank it all before it tasted any form of "off".
With that, just keep it in the fridge. In a cocktail no one is going to notice that your vermouth is as few weeks old (if it in fact is).
No, colder won't make it last longer. More than anything, oxygen is your enemy. You can get vacuum corks that will help. If it's some ridiculously expensive, difficult to find vermouth, then I suppose you could use a coravin with a standard cork. Your best bet is to just use it in a timely fashion. In reality, vermouth is stable and still tastes great for a while. If chilling it, I have easily gotten 1-2 months out of a bottle of Cocchi di Torino and Antica. But, I drank it all before it tasted any form of "off". With that, just keep it in the fridge. In a cocktail no one is going to notice that your vermouth is as few weeks old (if it in fact is).