We are encountering this problem quite frequently - a student sends a message in one of our message-groups using the mobile app, and the message gets repeated after a while. Often more than once:
It also happened to me (the admin), and I remember it happening after I clicked a push-notification that took me to the same conversation, but I could remember wrong.
This problem is also described in the following post: https://moodle.org/mod/forum/discuss.php?d=362959
and here the problem was found to be their messaging server (no further explanation...). But we are using the default Airnotifier messaging server with the default moodle mobile app and pretty much all related settings are left at default, so this answer doesn't really help...