Why does Illustrator keeps activating the same fonts that have been activated earlier?

I find an adobe font I like for a project and activate it. Next day I come back to the project and open Illustrator without an internet connection and find that font is missing. It won't come back unless I connect to the internet and the font is activated once again by Creative Cloud.

My question is why don't fonts once activated stay activated? Why is an internet connection required every time to activate them?

It happens with some fonts and doesn't happen with others. Is there a way to permanently download fonts I use often? I don't like to stay online all the time while working because of various reasons.