Short of trying it on a WiFi with a known good connection theres not much to help you with.
Your trying to use the app on a cellular network, with lots of other users, so if you have great thruput one minute the next you might not.
LTE rollout is still in its early stages and i have noticed in my area with my GS3 on LTE my speeds can fluxuate.
Thats about the only thing i can think of. I have used the TWC app to watch tv (on my home wifi) and ESPN Watch and not had any issues.
Basically its either an issue with the app not liking the hardware or the data coming into your device not having enough bandwidth or a bottleneck.