Save an analysis by clicking the Save
button 
on the ArcMap standard toolbar or by selecting Save from the ArcMap File
menu.
After you finish working on an analysis, you can save it and exit ArcMap. An analysis is saved as a .mxd file. Dynamic layer information is saved in an associated .mdb personal geodatabase A geodatabase stored in Microsoft Access database format that supports many readers and a single editor. file within the analysis folder.
The data displayed on a map is not saved with it. Map layers reference the data sources in your GIS database. This helps to keep map documents relatively small in size. The personal geodatabase saved with your analysis includes all of your dynamic layers but, like ArcMap maps, map layers only reference the data sources in your GIS database.
In general, it's a good idea to save your analysis periodically while editing it just in case something unexpected happens.