Following up on a post from earlier this week, I've figured out the issue. At least in the Android version, if you try to report a cheater during someone else's turn, the report doesn't go through. It only goes through if you report during your turn.
This means you have a Hobson's Choice of playing to stay alive or reporting the piece(s) of garbage.
It's not working that way for me. Yes, it closes when a turn ends, and yes, when I go back my text is still there. But if I click SUBMIT during someone else's turn, the report doesn't actually go through, You can tell because the REPORT button will remain red and not gray out like it does when a report has been submitted.