Light, temperature, and humidity are the enemies of just about anything you want to preserve.
When storing something long term, I wrap it up in acid-free tissue paper to prevent it reacting with other items or the container. I still use plastic bins and bags because of price and availability, but I sometimes think metal or "good" cardboard boxes would be the best... except for air circulation.
Degradation of the plastic and vinyl, out gassing or plasticizer leakage, just seems inevitable. Like an archivist, you've got to monitor a collection. So I check and repack every now and then, which is a great excuse to play with things, remember "oh, I have that!", and get 'em out in circulation for a while. Ponies are meant to be enjoyed.