Yes!! This happens to me. I got my box within the last few months, billed by BT, and notice that quite frequently the frame rate drops for a short amount of time before going back to normal - extremely annoying. I watch motorsport and you really notice it. However, your issue seems more severe so unsure if we're experiencing the same issue.
I'm running the box into an LG C4.
To be honest, I only watch recorded content on the box, everything live I watch on the TV apps as the frame rate is fine (showing it's an issue with the box/EE TV's service), and I know that if I report the issue to EE/BT they will not acknowledge it as a consistent issue on their service and would not resolve it, as you've proved by now being on your 3rd box.
This sort of thing always happens with big organisations - you see it on forums that numerous people experience the same thing, indicating there's something that actually needs resolving, but you report a fault and they just treat it like an isolated issue that can be sorted by turning it off and on again, and failing that, a new box, which doesn't help. It needs investigating properly but that would involve admitting there's a deep rooted issue with their service.
