The random flashing LED is usually caused by the battery voltage dropping below 2.8V. The battery that came with one of mine died really fast, but the others have been fine.
I've also found that the battery level sometimes goes back up after pressing the button device's refresh button.
In general, how is the performance of the Doorbell 6? Is the range between the button and the siren pretty good? I've been debating getting one. I've had a lot of problems with the honeywell doorbell I've been using for a couple years. Been trying to find a replacement.