What user troubleshooting do you suggest? I've experienced the same issue on an iPhone 6 running iOS 9. Upgraded on release day, have erased all content and settings once; the issue happened before performing the full erase, and has happened afterwards. It occurs at random intervals, and with various conversations in Messages; some longer conversations with lengthy history, some with only a handful of messages in the conversation. Leaving the app with a single Home button press, then returning, does not resolve; thus far the only thing that fixes, as WESTIA indicated, is to double-tap the Home button to open the app switcher and swipe away Messages to force quit the app, then reopen Messages.