Do you become unhappy when happiness disappears? Do you become unhappy when happiness disappears? Or is there some other state of mind between happiness and unhappiness?
When you are hungry and you take a first bite of your favorite meal, the happiness in the aspect of a pleasant feeling that you experience is not actual happiness, it is not in the nature of happiness: it is contaminated happiness. That pleasant feeling you experience is merely a relief. You experience the first bite as [contaminated] happiness only because it relieves you from a greater suffering (i.e. hunger), not because it is in the nature of happiness. It is actually in the nature of suffering; it is suffering of change (a quiet subtle form of suffering).

As Tsongkhapa puts it in the Middle-Length Lam Rim:


  At present most of the happy feelings that increase our attachment are
  minds of happiness that arise with respect to a relief of suffering.



If you eat when you are not hungry, there is no such relief, no such pleasant feeling, no such experience of "happiness in the aspect of a pleasant feeling", and it is experienced as suffering  of suffering (a quiet gross form of suffering). You are not mislead to conceive of the object as being in the nature of happiness.



There are three types of equanimity. The first of the three is 'equanimity feeling', which his neutral feelings.  Furthermore, when pleasant feeling arise, you wish to associate further with it. When suffering arises, you wish to be separated from it. Tsongkhapa writes further:


  That which is neither pleasant nor suffering is that which, when it
  arises, neither of the two wishes occurs.



You can think of it this way: you enter a crowded room, you look at people and you immediately have “I like this one... I like that one... I don't like this one... and so forth” in dependence upon pleasant and unpleasant feelings. There also will be plenty of people you will not have really noticed, you are indifferent to, your attention wasn't drawn towards, because of neutral feelings.

Another more abstract examples of arising of neutral feeling (which is other than neither-pleasant-nor-unpleasant feeling arising in the 4th concentration of the form realm) is: the conception of the body as permanent , that produces neutral feeling and increases ignorance. Tsongkhapa also adds in the Lam Rim Chen Mo that:


  In the case of [these] neutral feelings, ignorance ceases when you see
  that they are impermanent, permanent, exhaustible, and perishable in
  nature.