Just til I get there. LOL, seriously Janet, its butter based so probably not all that long. Are you saving it for something? If you are the better bet is to freeze it. Otherwise, a couple of days, not more than a week. I would think. I honestly can't answer with any authority because shortbread lasts one day max around here. And if its brown sugar shortbread...less than that. Lifespan in hours.
You're only given a little spark of madness. You mustn't lose it. Robin Williams Alix
A friend oversees has asked for a care package that includes this holiday standard. I usually make it this time of year with a little ground cardamom and lemon zest. The rest of the recipe is the usual butter, sugar, flour combo.
Just like bread, store your cookies in a paper sack - NOT plastic! (They'll go soggy right away if stored in plastic. Paper allows them to breath and keep their texture longer.) They'll keep 3-4 days on the counter before the humidity changes them to the point you'll notice. As Alix says, freeze them if you want to keep them for very long.
"Food is our common ground, a universal experience." - James Beard