Solvent Evaporation
Since these touch-up paints are usually based on modifed thermoplastic acrylic resins, the shelf-like is influenced by viscosity increase due to solvent evaporation more than any "chemical" change - at least in the short term.
Frequency of opening and closing the bottle as well as environmental storage conditions will have an impact on useable shelf life.
As the previous poster indicated, as the viscosity increases the paint becomes harder to apply and exhibits decreased flow. The various brands of touch-up paint have somewhat different solvent blends in their formulations. "Most". however, are soluble in acetone. Acetone is a very fast evaporating solvent and will lower the viscosity faster than most solvents.
When your paint gets thick, try addig a few ml of acetone (nail polish remover) to improve flow.