I just came across this:
Make it a habit to save your work often when working on your Maya projects. In that way, you can always open an earlier version of your work should you make a mistake.
Maya refers to everything you’ve created in your workspace as the scene. This includes any objects, lights, cameras and materials associated with your working session.
To save your Maya scene
1.Select File > Save Scene.
A file browser appears, listing the GettingStarted project directory where you can save your scene.
If the GettingStarted directory does not appear, you need to copy the GettingStarted folder and set it as your Maya project. See Copying and setting the Maya project.
2.Within the GettingStarted directory, double-click the scenes folder to open it.
3.Type: Lesson1 in the file name text box.
4.Click Save.
Maya saves your file to the scenes directory within your GettingStarted project directory. Maya automatically saves the file with a .mb file extension. The .mb file extension indicates that the scene was saved as a Maya binary file: the default file type for a Maya scene.
This may be of more help to you in the future than at the present.
http://mayastation.typepad.com/maya-station/2010/05/autosave-function-in-2011.html
Or this
http://www.andrewandoru.com/2009/02/20/labs-maya-recover/
It turns out that you have to turn this on in Maya.
If you exported it instead of saving your project maybe instead of opening the file directly, open up a new project then "IMPORT" your file into it.
I know I'm not being very helpful. I switched to Blender since I can't save my projects in the free version of Maya and it costs too much (I'm poor). Plus Blender has the option to use Maya's controls which I already learned.