I wrapped some buttermilk biscuits in a kitchen towel and kept them in the pantry (they were baked two days ago) but now they dried out and turned to some teeth-breaking biscuits! Where and how should I have kept the extra fresh?
Biscuits are notorious for that; they're best eaten right away. If you want to preserve their original texture longer than 12 hours (yes, that short of a time), your best bet is to freeze them as soon as they are cool and eat them within a month or two. Wrap them as air-tightly as possible.
You can pop the frozen biscuits in a moderate oven or unwrap and give them an hour or so on the counter to defrost, then warm them. Either way, it's best to serve them warm, they will seem softer and fresher that way.
If you've found a recipe you like and think you might want to make them frequently, mix the dry ingredients for multiple batches. If you can weigh the dry mix that you have just mixed, then you're golden. You can make as many or as few biscuits as you want anytime just by using the same proportion of dry, fat and liquid as the original recipe. You can easily make a single biscuit that way or feed a crowd.
Another option is to make your biscuits in advance, freeze the unbaked dough, then when you want them, only bake as many as you plan on eating. King Arthur Flour has a pretty good baking blog with a specific recipe and some tips, but the short version is that you just make the whole batch of biscuit dough, form them into biscuits, then freeze the unbaked biscuits. When it comes time to bake them, just extend the baking time a bit (around 25% in my experience, though it depends greatly on the size and shape of your biscuits).
I am not sure how people are only getting their biscuits to last for 12 hours before drying out... but that is not my experience. I seal my made-from-scratch buttermilk biscuits in a ziploc baggie (take the air out) and they can last for three or four days before drying out to the point where they're no longer good.
Don't wrap them in towels once everyone is done eating them unless you want them to dry out very quickly. Put them into that bag as soon as they are cooled and you start doing clean-up from your meal. Also, buttering your biscuit before microwaving it to reheat it can help to re-moisten it further.