I know from these answers that privileges are lost after dropping below the threshold for required reputation.
I've done that, and kept my privilege, though.
I used to have more than 1000 reputation on Meta SE, but I've now dropped below 1000 due to starting bounties.
However, I can still see vote counts in the Android app.
If I understand correctly, I should no longer be able to see that. I've tried with a number of posts, and it appears that I can still see vote counts everywhere on Meta SE.
Of course, I don't personally mind that I still have this privilege, and I'm not complaining. But I thought I'd report it.
FWIW, I tested this with my iPad too, and it does not appear to be a problem in the iOS app.
Update: I've now confirmed that this goes the other way around as well (when you gain 1000). See my answer for details.
I have 1.0.85 of the app, which is currently the latest version in the Play Store.