I have a Wired Doorbell Pro (Video Doorbell Pro 2) connected to our indoor mechanical chime.  The Ring device triggers the indoor chime only on every other push.  It doesn't matter how long the time period is between the pushes -- it can be a minute, an hour, or overnight.  If the Ring triggers the indoor chime it will not trigger it on the next push.  On the push after that it will trigger the indoor chime.  On those pushes where it doesn't trigger the indoor chime the Ring device itself gives its own three-note tone and it sends an alert to my phone through the Ring app, and the "mute" push is recorded, along with the related video, in the list of events in the app; it just doesn't trigger the indoor chime.  The next push will.  I wanted to check if the problem was with the indoor chime so I disconnected the Ring device and hooked up a regular doorbell; that doorbell triggered the indoor chime each time it was pushed.

I contacted Ring and they eventually decided that it was a hardware issue with the Ring device.  They sent me a replacement device but the same thing is happening.

Any ideas?