What apps are trying to connect? Most will poll occasionally to check for messages/notifications like Facebook, Twitter, Instagram, etc. or email and text, but it shouldn't be transferring enough data to cause interruptions.
The only exceptions I can think of would be an extremely slow internet connection (2G or EDGE), a large number of apps all trying to sync at the same time, or huge data transfers like backups, app updates or OS downloads. Maybe streaming media or media downloads?
If you know the apps that are causing the problems, listing them would be helpful.