So taking a cue from my wine storage, and seeing as vermouth is a wine product I use the same principles to some extent. Back when I started drinking and collecting wine I had a small problem in that I was the only wine drinker in the house and being 115lbs meant a glass or maybe 2 was my limit when drinking on a week night. My fellow oenophiles told me their method for storing a better wine to enjoy at a later date. I bought a couple of bottles of wine that were offered in a 375ml bottle and when I'd drunk that wine (actually I poured most of them down the drain as they weren't worth the calories, and I did go cheap after all as my final goal was the bottle). I removed the labels and ran the now empty bottles through the dishwasher. I have a half dozen of these empties in my cabinet in various colors for identification purposes. I just opened a fresh bottle of Carpano Antica Vermouth and poured half the bottle in one of the clean 375ml bottles and sealed with a Vacu Vin wine saver. This bottle gets put in my backup refrigerator where it will be undisturbed until needed while the original bottle gets it's own Vacu Vin top and is in my main fridge for current rotation. It won't last indefinitely this way, but I do find the back up bottle is plenty fresh when I need it.
Your best option is to buy your vermouth in smaller quantities, but when that isn't possible this is a great option.
*A good source for bottles are the little cheapie bottles of wine you will find at World Market or the grocery store that are intended to go in gift baskets. These are even smaller than 375ml and are good for putting up vermouth in even smaller amounts. I buy these little bottles and keep them around for cooking and keep the bottles when they're done.
I read about this interesting way to store vermouth and it works really good so far. I have the same problem as you, I don't drink a lot and travel for work so I don't go through liquor very quick. Now, vermouth usually is not that expensive, so buying a smaller bottle every week or so would be a good way to solve the problem. However I do from time to time find some interesting harder to find vermouths on my travels so I struggled with what to do after I open them.
What I found was the simple water bottle. I simply rinse out a couple of empty water bottles and pour the vermouth into them. Then before putting the lid on I squeeze out the air to eliminate the head space. I then put them in the fridge and as I use them, squeeze out the headspace before I put the lid on. So far I am very pleased with the results.
I do not find I have any plastic taste and the shelf life using this method seems to work just fine by the time the bottles go empty.