I have the TV Anywhere app on my I-phone and it works superbly, rarely crashes and is fine to use.
I also have the app on my Kindle Fire and it works terribly on this.
I mainly use it to watch BT sports channels, Eurosport and occasionally ITV4.
On the BT sports channels it brings up a message "problem streaming this channel" in a box that you only can remove once you go back to main menu. This usually happens within about 5-10 minutes of starting to watch it. On Eurosport & ITV4 it is not as bad but still happens roughly every 30-45 minutes.
I've mentioned this on twitter to the support team and get the standard responses about any problems in my area (there aren't). Have you completely closed the app and restarted (yes many times). Have you uninstalled and reinstalled the app (Yes and this doesn't fix it).
From what my friends tell me about Sky Go this app appears a lot better.
Are there plans to put an update to fix this on Kindle / Android devices as I feel a bit cheated with the app as it is currently.