Mindfulness and Pushing Away Emotions With objectless mindfulness, if I am in a bad mood the mood perseveres. I just observe the bad mood but it doesn't easily stop. 

However, if I applied concentration on an object such as the breath, the mood immediately dissipates and even sometimes vanishes.

Does strong concentration repress emotions, or does it process them in a healthy way? In other words, does focusing on the breath still permit the emotions to be experienced naturally despite an absence of thought or feeling?
With objectless mindfulness, if I am in a bad mood the mood
  perseveres. I just observe the bad mood but it doesn't easily stop.


This may be because the attention you're giving to the bad mood is the wrong kind of attention. There may be a clue in you wanting for the bad mood to easily stop. Observe with no anticipation for anything.


  However, if I applied concentration on an object such as the breath,
  the mood immediately dissipates and even sometimes vanishes.


The dissipation of the mood by shifting focus may be a further clue to the mental proliferation that you could be adding to the 'watching' of this bad mood. 


  Does strong concentration repress emotions, or does it process them in
  a healthy way? In other words, does focusing on the breath still
  permit the emotions to be experienced naturally despite an absence of
  thought or feeling?


It doesn't need to be strong concentration. One just needs to simply switch focus to something else. The something else can become a further problem like an escape though. Notice breath, movement, objects, light gradients... There are many wonderful harmless things to remove us from mental anguish. This is, indeed, healthy and not a repression technique.