If you want to store your wine or cider outside of the fridge without using preservatives, it's important to remove all the yeast and sediment that's at the bottom of your wine.
Not only can it impart off-flavors in your wine as it ages, but it will also start to re-ferment and re-carbonate when stored at room temperature. You'll want to avoid that so that the cork from your bottle doesn't unexpectedly pop off.
So, to make sure your wine is safe for room-temperatures storage, just follow this chart! The process will just take a little more than 2 weeks.
As an extra precaution, many people prefer to add preservatives to their Brewsy. If you'd like to do that, you can read about it here.