Multiple tea infusions and caffeine concentration
This study specifically addresses the question regarding multiple infusions:


  Results for all kinds of tea samples showed that the second tea
  infusion contained the highest contents of caffeine, catechins, and
  gallic acid when bag teas were steeped in 70°C water.  It was different
  from that steeped at 85 and 100°C, the highest contents existed in the
  first infusion.  These compounds decreased gradually in later
  infusions.


The paper measured 8 successive infusions on a variety of teas.  You can see how caffeine content varied exactly in their data.