I have been having this same problem for a while now. Just watched Olympus has Fallen and once again the sub-titles stuck continuously, had to stop the movie a dozen times and resume.
What I find strange is that Apple have not officialy withdrawn support for Gen 1 Apple TV and yet we have a clearely defined bug and they are making no attempt to either fix it or provide any feedback on what they plan to do. I understand that they are not bringing new features to Gen 1 but the existing software should be free of known bugs. Clearly this is not the case.
I am also an Apple fan with just about every product they sell in our home, iMac, 3 Mac Book Pros, iPhone 3GS, 4, 4S and 5, iPod Touch, about 5 iPads. At this stage the only option I can see is moving to the new Apple TV, I suspect there may be a new one on its way so will wait until the next round of announcements. Not sure what I loose by moving to the new Apple TV but the Gen 1 has been very good so seems crazy to just dump it now over what appears to be a small bug.