How long can I store cooking wine?
The trick is that you won't want it to oxidize (although, red wine needs to 'breathe' to reduce some of the tannins, which is why @DanielBingham said it might improve.)  So, if you just need to hold it for a few days, store the bottle upright (minimize surface area exposed to air), and not on the door of the fridge -- it'll get jostled and mix air into it.

They also sell gadgets that inject nitrogen or other non-oxygen gas into bottles, or things to suck out the air, etc.  But if you're not much of a wine drinker, from your earlier comments, I wouldn't bother.  (hell, I don't even know if they work).

Oh -- boxed wine will last longer -- because there's a bag inside the box, when you pour out wine, the bag deflates, so air doesn't go back in (or not much of it).  You can hold boxed wine for a week or two, maybe even longer without problem.

If you're not much of a wine drinker, and only cook with the wine -- you might want to consider freezing it -- as with everything else -- an ice cube tray, freeze, transfer to zip-top bag.  Then, when you need little for a sauce, you can just thaw out of a cube or two.  It might not be as great as "fresh" bottle of wine, but if you're cooking with it, most people won't notice the difference, and it'd still be better than a dedicated "cooking" wine.