Re: Fed up with my Ring Pro
"There is a button at the front door, connected to the LAN over WiFi"
If you are after a fix, nine times out of ten, the issue will be your wifi connection. Ring and a number of other IoT devices are low power devices and often aren't able to transmit at the same power as the WLAN AP they are talking too. The IoT device will receive a signal but fail to reliably transmit back to the AP.
The simplest test is to check signal strength with a mobile phone app - if the signal is under "good/orange/-75dBm" (if there is no interference from other sources including neighbouring wifi) or "excellent/green/-60dBm" (if there is interference that you can't fix by changing the wifi channel) due to the number of wifi AP's you can see, you will likely need to move your wifi AP closer or get a booster. If connectivity is intermittent, its likely to be an interference issue