We usually buy our potatoes from one of the farms, they keep much better and are cheaper to buy. 25kg bags and keep them in the paper sacks, after spreading out in fresh air to make sure they are dry, then into smaller hessian bags for indoors. Store in the shed for months, the ones we are using at the moment were bought in October.
But like you say the odd times I have to buy from the supermarket they never keep for long and sometimes are not so good when you peel them - even when they look alright. I do always remove them from the plastic bags, as with all veg.