so uninstall re-install, clearing the app's data and cache, rebooting the phone, in your phone's settings checking to see if notifications is set for sound.......none of these suggestions worked for you?

i also found this as well:
https://support.ring.com/hc/en-us/articles/115005889983-Android-Apps-that-Conflict-with-the-Ring-App

apparently there are some known apps that will interfere with the app's notification

 

well that is the only thing that i could find. i would try uninstalling AVG and see if that helps. to be honest i do not see a need for antivirus on an android phone.

 

Are you sure the problem is with your phone or the Ring app? Do you have any other mobile device or computer to confirm the problem is definitely with your phone or app? If other devices are working OK with your doorbell it's probably not an issue with your S6 but the Ring doorbell or perhaps it just needs to get reconnected to your home network. If you check your routers settings page there's most likely going to be a menu option showing which devices are connected to it, is your Ring doorbell listed there?

 

well try uninstalling the avg and see if that works......like i said. if it is still a no go then contact ring for more assistance.

 

If other devices are able to work correctly with your Ring doorbell that at least that confirms that it's still connected to your home LAN, but the issue that needs to be addressed is the failed link between your S6 and your Ring. Try restarting your router.

 

Hmmm maybe it's because you have an older device. Has the app been updated recently? If so maybe the new update will not work properly. As devices get older app developers are forced to keep their apps updated to the latest android version make it harder for things to work on older devices.

Also you may want to try and get into contact with Ring and see id they can help.