I had a similar problem at home (TiVo HD + Premiere) but only on a few channels. I disconnected the THD & splitter, which helped but did not resolve the situation. I swapped out RF cable with no change. I called Comcast out to check the signal on particular channels and they did find the need to boost my signal a bit, but the problem still showed up intermittently (and wildly unpredictably).
Then I brought another Premiere box in and it did not have the problem when using all of the exact same connections that the first one was using. It's only one data point but you may have a similar hardware issue.
Then I brought another Premiere box in and it did not have the problem when using all of the exact same connections that the first one was using. It's only one data point but you may have a similar hardware issue.