There is a very long discussion of this topic on Amazon.com. Sony BRAVIA models more than five years old may not work perfectly with Amazon’s Fire TV stick. I have this problem and I’ll mention my workaround.
My Sony TV model is BRAVIA XBR 32XBR6. I suppose it’s about five years old. I also have it connected to a Sony Blueray player, which can also play Amazon Prime, Netflix, Hulu Plus, etc. But it isn’t nearly as well designed as the Fire Stick and so I bought the Fire Stick, which has better WiFi support and a faster user interface.
Initially the Fire Stick appears to work with the TV and all is good.
Second day: same thing. All is good.
About the third usage, however, and when playing on-demand content I hear what I’m trying to play but I only see a blue screen with the letters HDCP. I think that indicates a digital copy protection mechanism has kicked in.
Powering down the Fire Stick doesn’t seem to work. Turning the TV off and on doesn’t seem to help.
In my case I had the option to switch to watch the same content through my Blueray player (which never displays this problem). Then next time I went back to the Fire Stick (usually days later) all was good.
So I became suspicious about cause and effect and I shortened the cycle.
Get the HDCP problem. Switch HDMI ports to the Blueray player (using the remote). Initiate the Amazon video service connection on the Player (but don’t bother to actually play anything). Switch back to the Fire Stick’s HDMI port. HDCP problem gone!
This solution was not too painful. I also have a Raspberry Pi connected to yet another HDMI TV port. I’ll see if switching to that will do the trick as well – that would be a cheap option that’s not too painful.
I never get this HDCP problem any more. The main difference is that I never use my Sony Blueray player for on-demand programming. The Firestick is superior so I always use it. I only use the Blueray player for DVD playback.
October, 2017 update
I got my birthday present – the updated Fire TV stick with Alexa voice remote, but on the same Sony TV. It does seem to work better. The old one was button press, nothing happens, button press, nothing happens, button press, finally it gets the idea. The new one does seem to be better about that.
A solution is offered to the dreaded HDCP problem for Amazon Fire Stick/Sony BRAVIA TV. More research needs to be done to reduce the solution to its essence.
Here’s the link to that lengthy discussion: http://www.amazon.com/gp/help/customer/forums/ref=cs_hc_g_pg_pg1?ie=UTF8&forumID=Fx1SKFFP8U1B6N5&cdSort&cdThread=Tx1A10FFQXCSZ2M&cdPage=1
Fire TV Stick (2017 model).