I have an LG phone (Viewty Smart) and it automatically disconnects from the internet when an application that was using it is closed. Furthermore, you can see whether or not you’re connected because a little globe icon appears at the top of the screen when you are. If there is no icon, and the manual suggests that there should be when connected, then I think you shouldn’t worry about it. If however there is an internet connection showing that doesn’t seem to be able to turn off, I would consult your manual or call technical support.