So here's the deal... Apple obviously did not QA (quality assurance) browser support at all. Maybe just some random passionate engineer got it pushed thorugh even though it was not a priority for launch. That's unfortunate that marketing and PM's (Product managers) did not feel it should be a first class citizen for launch.
What is to be done now?
Given that apple support has not responded to any of us, I'd say anyone wanting browser support for apple tv + should just cancel and provide feedback or file a support ticket. Honestly I don't think they really care. This was an initiative pushed through and I don't feel like anyone is at the wheel. Great follow through Apple! Dooming your video streaming service before it could even begin!
As to the god-honest-problem here? It's possible it's a session timeout set at around 12-15 minutes. But I'd suggest it's more likely a DRM issue where some apple exec has decided to be over-zealous with the browser restrictions cause they are so paranoid about their stuff being pirated. Who is hurt by DRM again? Is it the pirates? No apple, it's always the customer. Netflix, Hulu, Amazon Video, HBO, and many others learned this long ago.
Apple, do yourselves a favor and hire some engineers from the other streaming services. You can surely afford to pay them.
BTW, I'm available for hire as well.