Should bitters be kept in the fridge? What about vermouth?

You always see these items out on the gantry at bars. But they are probably going through them a lot faster than I am.

Is there a "threshold" alcohol content under which a beverage should be kept in the fridge if you plan to keep it open longer than a few days? Wine only keeps a day or two before it goes off (even with the air vacuumed out), but spirits can keep for months or years.

I'm fairly new to home cocktail making.