I am also having similar issues. Funny thing is, I side loaded the tablet version and it worked fine. There are a couple of things I am currently wondering...

Although I bought the device in the US, I am streaming with it in Canada. Wonder if Netflix is getting confused with my Canadian IP.

Since the TV app is supposed to stream in higher quality, Netflix is pickier on the device it runs on and checks DRM, which may even run as deep as the HDMI connection. I.e. if a well negotiated connection with the TV is not established, it drops the stream. I'll be able to test this soon.

Any other insights?