I have created a simple transition from an animation to another using the animator state machine for mecanim.
I also modified the transition in the inspector by moving the begin transition slider and the end transition slider.
I saved the scene, and all the information has been saved.
When I close unity, open it again and the scene and start playing the scene, the transitions play as default but do not show the modified behavior I edited before. Also, an dthats the most obvious thing, the progress bars for the animation nodes in the animator window (blue progress bars in the nodes) do not appear.
Everything comes back as I click the Character node in the Scene Hierarchy once, and stays as it should.
Paulo is right. Without setting an exit time, mecanim cannot know when the transition will occur so the placement of the slider will not matter as it can happen anytime. That is why its not remembering the setting - as that setting is not used unless there is an exit time condition.
If you want a more detailed explanations check out these other threads with the exact same question :
using 4.0.0.7