Here is a good sequence of troubleshooting steps for this problem (which can also be found elsewhere).
- Restart phone
- Clear app cache
- Clear app data
- Uninstall then reinstall app
I have tried all of these troubleshooting steps, and none of them deleted my conversations. They are probably backed up somewhere.
This problem has happened to me twice. The first time, I think I solved it by uninstalling and reinstalling the app. The second time, I know that restarting my phone didn't fix the problem. What did fix it was both clearing the cache and clearing the data. I didn't try just clearing the cache. If I am so mildly unfortunate as to experience this problem again, then I should check if just clearing the cache suffices.