As your MapInXL map is part of your Excel 2007 document, just like the other components (charts, pictures, drawn forms, etc.), every map included inside your document will be available when re-opening it. You can use the “Save as…” function of the Office button to save your Excel 2007 document as a “.XLSX” file.
You can also get your map out of Excel by exporting it : in the MapInXL ribbon, the "Export your map" button from the "Data" group offers you to export your map to the clipboard, to paste it in another application, or to save it as a picture file (GIF, JPEG or PNG).