Shelf life may indicate colloidal stability, though you can allways just shake the sample if it drops to the bottom of the vial. If the nanopapricles change in size, shape or irreveribily aggregate this may limit the shelf life.
Article Characterization Techniques for Nanoparticles: Comparison an...
For a compherensive review of methods to study nanoparticles. Table 1 & 2 summaries methods and the info they can provide in relation to NP size distribution, shape, surface omposition, zeta potential, etc.
Commercial example shows data obtained from several methods:: https://tools.nanocomposix.com:48/cdn/coa/Gold/Spheres/NanoXact/AU40-NX-TA-ECP1416.pdf?121%20905
This data sheet confirms products identity and key properties, which can be re-checked at future times to confirm products stability, though with gold UV-visible spectrum is sensitive enough, as changes in aggregation show in the color of the gold colloid.