Why don't OTA firmware updates work with my system?

Over three years and three base stations, I can't remember the last time my system properly received a pushed OTA firmware update, and this pattern has continued even with the latest base station replacement I just installed on the system which is currently running the v2.3.10 of the base station firmware.

Can somebody help me get this resolved? It seems to be a problem outside of the base station hardware and whatever is going on is still on problem on v2.3.10.

A customer support agent told me today that an update was available for my system and she pushed to my devices, but I still do not ever see the gear icon on the keypad or receive any notification in the iOS app. This has been a problem with my system for more than a year now, and replacing the base station and keypad hardware does not seem to have resolved the issue.