The official word from Amazon to get an update is to press the Mic button so that the top ring is red. Leave it that way for a few hours and the update should come through.
The reason is simple. The Echo assumes it is in use if you are speaking to it or if there are other noises or sounds near by, whether it's from a TV, radio, neighbors, pets, traffic noise, loud refrigerator/appliances, etc. After all, the Echo is constantly listening for its wake word. If you mute the Mic, it will hear nothing so it will assume that it is not in use. When it is not in use, that is when it will go out and fetch updates.