I don't have the Roku tv, just the Roku device, but my screen is going black too, the program will play for 40 seconds, then go black, then it comes back on and plays for 40 seconds then black again. I timed it last night. This only happened after the 10.5.1 update a few weeks ago.
I thought i needed a new tube/lamp for my tv but picture and color was fine. So i had tv off for a couple of weeks til i got the new lamp. Last night i decided to try the tv, and that's when i discovered the shutting off thing. Can you check to see if you have the new update, maybe that's what's causing your tv to go black too.