UV menu dissapears after clicking off of it whenever you add something like a cylinder or a UV sphere, a menu pops up at the bottom that lets you change things like number of faces and such. But as soon as you click off of it that menu disappears, how do you get it back or where is that menu after clicking off?
That menu is there to help you define the parameters of the object, however, once you move or edit it, that object will no longer be able to be defined. Any action you take on the object, including a simple move or clicking to another object, counts as an edit to the system and stops it from being defined.

It's a catch all mechanism.