Alyce,
On cases like this, try wiping it down with a slightly damp cloth to remove dust. Then apply Armour-All, following their directions. This is what my husband has done for years with microscope accessory cases, and he has wonderful luck. I know that is what was done to my GE case, but can't get at it right now to check on how it is holding up.
As always, try anything on a small, hidden area first. Over time, temperature, humidity and sun exposure can change how the same material reacts to treatment.
Dianne