I managed to find a computer I could download the Player version onto to check this out….
So you are not actually closing and reloading Kontakt Player or closing and reloading the library, you are trying to reload a saved project that contains this particular library.
This is indeed a limitation of the Kontakt Player rather than a problem with the Kontakt Player, which is essentially a demo version of the full version of Kontakt.
If anyone else is perplexed by the Kontakt Player search for;
Kontakt Player Demo Mode – Explained by bedroomproducersblog written by Tomislav Zlatic