If you have Autodesk products on your Mac, I would NOT rename the Application. I would "Make Alias" of it and rename it to whatever name you wish. Also, you can add this Alias to the Dock so that you know which version you want to launch. This is very helpful if you have many versions of the same product.
Make Alias [Mac] = Create Shortcut [Windows]
In this scenario, Maya 2013 was functioning but when you label an older different version of "Maya" to "Maya2011", it can cause some licensing issues because some of the paths for the product are hard coded when you Show Package Contents.
[Please click on image for demo animation.]
Basically, if you rename everything back to the default name i.e. Maya, everything should behave as expected.
Thanks to Steven Weitz for confirming this very interesting behaviour.