Illustrator (25.2.1) will not save any of my preferences for units. Every time I set the units to inches and quit Illustrator, it reverts back to pixels when I open it again. It saves all of the other preferences I've changed besides units.
If this is not related to opening a document, then it might be preferences corruption.
The units are a document based setting and what you set up in the preferences does not affect existing Illustrator documents.
But it should keep the settings in the preferences. You could try and rename the preferences folder. Illustrator will then create new preferences. https://helpx.adobe.com/illustrator/using/setting-preferences.html
Once upon a time (to be specific the CS apps time). You could change the unit in the Preferences without having an open document, quit the app, reopen it and the settings were kept.
As far as I can check (CC2017) this does not work any more, the old settings are kept.
Not that it matters much, creating a new doc with a different unit will change the prefs unit setting.
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