How long does boxed wine last?
In my house, three litres can do me for almost two days if no guests show up. (Kidding!)
I'm assuming you mean a new, sealed box rather than one that's been opened. If it's open, it should stay fresh for four to six weeks. When still new, a standard three-litre boxed wine should remain in good condition for roughly nine months. Some in fact come packaged with best-before dates, so check your carton.
The industry term for this packaging, by the way, is bag-in-box. That's a reference to the plastic bladder inside that contains the wine. As liquid is drawn out from the spout into your glass, the bladder collapses to keep out corrosive air. A very slow trickle of air does, in fact, seep in, which explains the short, four-to-six-week lifespan of an opened box. But in this regard the packaging beats glass bottles, where the wine tends to start tasting dull within a day or two after it's uncorked or unscrewed, depending on the remaining fill level.
Wine in boxes generally is designed to be consumed young and fresh. But if you've accidentally "cellared" such a product in a closet or under the kitchen sink for longer than the intended drinking window, don't worry much. It may just end up tasting stale rather than plastic-y.