Same happens to me. It'll stop for a few seconds and I still hear the movie and then it'll start again. It does this for both live feed and movies on demand. It also buffers quite a bit which gets very annoying. I think it's my internet connection but also I have heard lots of problems with the app too.
I have been having problems with it also It used to work on my Nexus 7 and then when my Nexus updated it now crashes every time I go to play a movie on the Watch TCM app. It still works on my lap top. The movie Private Lives will not work at all on my lap top and I love that movie and have not seen it in a long time. The TCM logo re loops over and over. I e mail TCM and they e mail me back and say they will let their tech dept. know and that is the last I hear from them and nothing gets fixed. I feel your pain. My lap top has ie and firefox and it works on fire fox. I also have flash p