I also don't refrigerate the fortified wines, but one thing you might want to invest in, for this, and many other things, is a
Vacu Vin. With this, a rubber stopper is placed in the bottle, then you pump out almost all of the air, and things store well forever, or at least until used. I use this on a number of things in my liquor cabinet, because, like regular wines, that air above the liquor can oxidize, and change flavor of things. I use it on my cognac, more expensive tequila, and a couple other things - most sugary things I don't bother, but I have had some things go bad (not enough alcohol!), so I protect those. They have way more expensive electric versions, but why bother? The hand model is incredibly cheap (maybe $3 more than when I bought mine, in the 80s), and the electric ones don't pump out any more (a friend got one when they came out, and it actually pumped out less, so she took it back!).
Vacu Vin
The reason I got mine is a funny story: Back in the 80s, when I would drink a lot of wine, when I would make French or Italian dinners to a lady I knew. Usually she would drink about half of the first bottle, but when I asked if she wanted more wine, and she did, she would then not drink much,
forcing me to finish the bottle

. After getting one of these vacu vins, I could save half a bottle or more, with little change in flavor.