You can do it in a similar way to keyboard, storing the state by yourself:


       enum States {None, GoingDown, GoingUp }

       States Current, Previous;

       void Update()
       {
               Previous = Current;

               if (thumbStiscks.Y>0.5) State = States.GoingUp
               else if (thumbSticks.Y<-0.5f) Sate = States.GoingDown
               else State = States.None;

               if (Current == States.GoingDown && Previous != States.GoingDown) 
               {
                   ....
               }

               ....

       }

Maybe a good idea using keyboard to change the Current state too.