I keep my polymer clay in several clear, sectional, plastic boxes, and some of it is very old, yet it's still as workable as ever. Well, the actual Sculpey is. Fimo is as hard as when I got it, and I avoid buying it because it's just too stiff for me to work with.
I'm not sure where I got the boxes originally, maybe at Micahels, or at White Rose, which went defunct decades ago. I keep the colours separated, and the lids snap on reasonably tight. My sister stores her polymer clay in the exact same boxes, and her clay is also as good as new.