The first batch turned out fine, but for this batch I cut the sugar down by 1/3 cup and didn't add baking powder. The resulting dough is so sticky (even after a week in the fridge) that it is hardly workable. What went wrong?
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It sounds like the dough is simply too wet, and you need to add in a bit more flour. Flour is affected by the moisture in the air, so sometimes you need a bit less, other times you need a tad more. Try mixing in more flour, a couple tablespoons at a time until it's much less sticky. Then wrap and chill it at least an hour or two, and see if that won't help.
Amount of flour is no doubt the problem, but it will be awfully difficult to mix it in at this point without overmixing the dough. I'd try handling the dough with wet hands, which will make it much easier to deal with, and baking as is. Sticking is rarely a problem with cookies, but I'd be sure to use parchment or a silpat with this one.