Hi,
FSHud uses a own proprietary format for his application and therefore you “fall back” to the default AIRAC cycle which is shipped with FSHud. We offer every addon developer a default cycle (at least one year old) for their initial setups (release date). In most addons, you can backup the cycles by your own but in that moment, where you re-install the addon you will fall back to the default cycle - that´s not FSHud specific. That happens also in LNM as an example …
But as I wrote, FSHud is special because the developer uses a own format, and also he is the responsible person for releasing the AIRAC cycle. We (Navigraph) offer him only a basic-file, which he uses to generate the proprietary format. What I know is, that it´s not possible to backup the FSHud cycles by your own - there is an workflow behind, where you need the server from FSHud.
… on the other hand, when you want to stay in sync between MSFS and your addons, you run into an issue latest with 2306 due the different sources and cycles between MSFS, LNM and FSHud (+ all your other addons, when you use some).
Cheers,
Richard