The shelf life of the finished wire can be quite long. There are some motors that were insulated years ago and they are still running.
When you have an unopened container of enamel it should have a fairly long shelf life. Your enamel supplier can answer this question. Normally you would not or should not purchase any more enamel than you would be able to use within a couple of weeks.
Again if the enamel is in it's original container as received from the supplier, storing it for several weeks or even months should not be a problem. Even if you have removed some enamel and then tightly closed the container, it should be ok for a while.
If you are storing it in an open container, the solvents will evaporate - rate of evaporation depends upon solvent and ambient temperature. If stored in open container, then you have to worry about the enamel , if hygroscopic, adsorbing water from the humidity in the air.
Shelf life for the enameled wire should be near infinite. There are thermosets and thermoplastic coatings. Once a thermoset is cured it doesn't change. Thermoplastics in some cases may continue curing while in the warehouse. There used to be some thermoplastics that were used to insulate wire used in oil filled transformers. Once in the transformer and its filled with oil, it didn't matter if the wire continued to cure.