As shared above, that this is happening with the latest version of the Adobe Reader DC on the latest OS High Sierra. So could you please confirm whether its started happening immediate after updating to the latest version or you had this problem earlier too?
Also, have you tested with any other document? If not then please do.
Try to Reset Preferences of application as suggested in help document. How to reset Acrobat Preference settings to default. (updated link)
For Reader DC you may try- close Acrobat Reader and delete ~/Library/Preferences/com.adobe.Reader.plist
With the latest version on High Sierra this issue has not been reported yet. However if you have experienced this then we need to check it at our end.
Let us know the update on this, if it still doesn't fix.
Thanks for your response. I installed the Reader after I'd already updated my OS to High Sierra—so I can't speak to its behavior prior to the High Sierra update.
I have tried this on multiple PDFs and I get the same result each time after annotating and saving, the PDF file loses its finder tag.
There is no "Repair Installation" under Help in my version of Adobe Acrobat Reader DC. Having just updated Reader DC again (2018.009.20044), the problem still persists.