If I forfeit Breaking News, will the tags stick?
In the latest FAQ from FFG the case of Archer, Amazon Industrial Zone and Breaking News is mentioned.


  If the Corp scores
  Breaking News
  and then rezzes
  Archer
  through a card effect, forfeiting the Breaking News, does the
  Runner keep the 2 tags?
  
  Yes. The conditional ability on Breaking News has not yet
  triggered, and it will not trigger when the turn ends since the
  card is no longer active.


So yes, the tags stick.