Session is disabled by default in SharePoint. One reason is the memory usage may be invoked by thousands of users accessing the system. Although it can be enabled and set to use SQL Server, it isn't a recommended or common practice with SharePoint.
If the goal is to persist the data so it is available after closing the dialog there may be other alternatives. The client object model in SharePoint 2010 allows for asynchronous operations to refresh the data. The dialog framework also does not issue a postback when closing that I'm aware of.
SharePoint 2010 Client Object Model, Part 1