You may want to first try some kind of solution of polyvinyl alcohol to make the material more supple. That should be low-risk and you can probably wash it off if it doesn't help.
Next up maybe white mineral oil which is clear and odorless. I suspect that hydrocarbon oils may be too much for it and weaken the material (the vinyl bond to the base fabric), so this should be tested first before regular use. There are also silicone oils that should help, and be relatively inert, so study those too.
Commercial products like Armorall may work but I've never used or trusted them so don't know. I've heard long ago that they may deteriorate car interior materials but that could just be urban legend.
Experiment with the item in worst condition and see if anything seems to work. Good luck.
Ed
