What is the shelf life of vermouth?
Opened, at room temp: A week or two without serious flavor changes.
Opened, but kept in the fridge: a month, at least.  (I'm still working my way through a bottle of dry vermouth with no noticeable degradation in flavor in ~3 months, ymmv of course).
Unopened: A year+ at room temp.  

Source: Serious Eats experiment