Your Surface RT has a gimped version of Windows on it which Microsoft hasn't been putting a lot of money into recently. HBO Go recently upped the required version of the Flash player and Microsoft hasn't (and may never) updated the built in Flash Player. This is why it used to work and no longer does. HBO even specifies that Windows RT isn't supported.
You also cant update it yourself since you have Windows RT, it's heavily locked down and I doubt Adobe is making special builds just for the special processor the tablet has it in.
Windows RT was apparently a fun experiment for them and they've nearly given up on it. So that leaves us with one screwed.