I have the same exact problem. Has this not been solved yet? I've tried literally everything and nothing helps, the only thing which "temporarily" helps once or twice a day is if I turn on and off the box with USB and ADB debugging but then after a few minutes it stops working again. I really hope they find a solution soon, I can see by the date of this post that it's a few months old now and nothing seems to have been done, why is that I wonder?!....
It looks like this problem is caused by the Fire Stick timing out and going to sleep. Your echo doesn't seem to be able to wake up the Fire Stick.
To see if this is the cause of your problem, just press a button or two on your Fire Stick remote control. Then tell Alexa to show the front door.
It's what 'officially' works for me.
You would have to make sure the Fire Stick on your TV is connected to the Echo device. I forgot what that's called.
Keep in mind, my Ring was working when I posted this question - I had set everything up and saw it all work. But after leaving things alone for some time it would no longer work when asked to "Show the front door".
If you've never gotten it to work in the first place you may be dealing with a configuration issue on your Echo device. Open the Alexa app and connect your Fire Stick to the Echo.
It really is a puzzle. I never had the problem before, it used to show the live feed on my fire tv whenever I asked to show the front door and then suddenly it now refuses to do so. Maybe it's an update on the firestick which causes it...
btw, my setup is this: Ring peephole doorview cam (Think it's called) and Firestick tv 2. Gen. And also I use it with an echo Dot 2. I have several other echo shows but I connected the dot directly through Bluetooth, doesn't matter though cause it's the same no matter which echo I use it with, the ring Doorbell will show live feed on the echo shows but not on the fire tv stick.
Purchased a new ring doorbell 2nd generation set it all up with no issues everything worked perfect with Alexa except showing the live feed on fire stick 4K on my tv..
I had all the identical issues as everyone else posted here it would start with the little dots then just going back to fire tv home screen..I rebooted relinked re everything with no joy.
"FIX THAT WORKED FOR ME"
THEN using the original fire stick 4K remote control I pressed the microphone button and gave the show ring camera commands while on the fire stick home screen and by heck it worked and showed the doorbell live stream on my telly that I never managed to do any other way..
then I tried using Amazon echo devices in the normal way giving the Alexa show ring doorbell and that also worked!!! it switch source to fire stick and showed ring doorbell feed live and with sound etc..wow.
all working as it should now showing every time...
Let us know if it works for you..