Backing up Viber chat logs
As your phone is rooted, you could use Titanium Backup to backup app and data. Then uninstall Viber, re-install it, check if it works, and use TB again to restore only the data.

Keep in mind that when a mis-configuration is the cause of your problem, after restoring the app's data your problem might be back. In that case, simply repeat the operation, but do not restore the data, if you want the app working again. Of course, in that case your chat history would be lost; but you might be able to manually pick the data from TiBu's backups.