Nearly all plastics are made from crude oil by manipulating the molecules to form long chains (polymers) and are not the most chemically and physically stable of materials. What you're seeing are the effects of some plastics deteriorating, with the polymer chains breaking up and forming shorter compounds (the shorter the molecules, the more likely they are to be liquid or gaseous). The main mechanisms are:
- Oxidation (reaction with oxygen in the air)
- Hydrolysis (reaction with water, mainly vapor in the air)
- UV degradation (caused by exposure to light, especially sunlight)
Heat will typically accelerate such processes. So to reduce degradation, keep the plastics in a cool, dry, dark place, ideally inside an airtight seal. But even that will not prevent degradation completely. You'll just have to live with the fact that things made from plastics don't last forever.
Note that modern plastics often contain stabilizers intended to prevent the degradation processes. It's likely (but not certain) that companies that produce more expensive gear will spend more money on developing stabilizer recipes for more long-lasting plastics and tests to find out which ones work best.
A definitive solution would be to get a suitcase not made from plastic, not even partially. Probably very hard to find and expensive, though.