How to keep downloaded curated data

There are two types of curated data in the Wolfram Language, the classic "paclet" functions like ChemicalData and the EntityValue Knowledgebase functions like StarData, and only the former supports the "Preload" mechanism. If the first item in the ref 'details' section of the ref pages says The specified "name" in XXXXData can be an Entity, EntityClass, or canonical name. then the function is a Knowledgebase function.

You can always save the results of StarData[] with a function like DumpSave or Save, and simply Get["file"] in a future session, though I understand there are plans in the works for all Knowledgebase functions like StarData to have a caching mechanism in the future.

In Mathematica 10.4.0 (February 26, 2016), StarData[] and similar, e.g. MinorPlanetData[], is now cached. It downloads only once, no matter whether Kernel is stopped or no. Partial download also is cached.

You used to be able to Preload paclet data

PacletName["All", "Preload"]

For e.g. chemical data you'd type:

ChemicalData["All", "Preload"]

See also this support article

I've heard rumors (but haven't tried it myself) that in v10 this doesn't work anymore.