The speed and quality of the video depends on the quality of the Internet, the Shutter App cannot influence this. Most likely, the location has a weak Internet connection, so there are several options to improve the situation:
1. Before starting the session select the mode with loading full-size photos after shooting. So, while shooting, you will only receive the previews and this will greatly facilitate your work and reduce the load on your phone and the Internet.
2. Check with the client/model for the type of internet connection they are using. For example, ask the model to turn off Wi-Fi on the phone or, on the contrary, turn it on.
3. If none of the options improve the quality of the phone's internet connection, try to find another location to shoot.
Note: We highly recommend before the actual photo shoot (if there is an opportunity) to test the location for internet connection and see how good it is there.