Hi ,
For qListView to remember the filter criteria, you need to set the "Session Name" property under Edit Display Fields in qListView's ezEdit dialog.
In addition to the Export tool under Actions menu, you can also consider an alternative method using our qExcelViewer web part to handle exporting data to Excel. You just need to provide the url to the page containing ExcelViewer in "Excel Viewer Url" property and configure ExcelViewer with the same Session Name you gave to qListView. You will then see a new button enabled in the toolbar which when clicked will export the filtered data to Excel, without loosing the current context.
Based on my testing in SP2010, both methods will let you export only the data returned by the filter.
