Please try the following troubleshooting tips:
Adjust the video playback settings within the app
Visit the app's "Settings" menu (the small gear icon on the top left of the nav bar) and enable the "Play Video Over WiFi Only" setting
Make sure you're running up-to-date software. The Acorn TV app requires iOS 8+
Visit Settings > General > Software Update
Disconnect other devices from your network
Delete and then reinstall the Acorn TV app
You can also check with your Internet provider to see if your capabilities can be improved. If bandwidth is not an issue, then please click "contact us" on the link at the bottom of the page to fill out a ticket, which will send us a diagnostic report that we can use to help resolve the issue.