Networking is a process rather than just an event. Networking events are part of the process but often thought of as the complete activity. The events that open the doors to enhance and facilitate networking serve as a door opener to make new contacts, renew and refresh old contacts and further build the relationships of those that are part of your network.
Networking events are a useful tool. They are just that, however, a tool. Often, however, they are relied upon as the main event wherein they make or break their networking success. It should be used as a time-efficient tool to making and building more contacts, but the relationships begun or enhanced there need to move outside of that arena in order for the necessary to occur to create the real magic of networking.
Connect at an event and use it as a spring board, but take steps to develop the relationship outside of that event rather than rely on that brief period to determine the fate of the relationship.