Can I activate Nim Deathmantle's creature saving ability more than once in a turn?
Yes.

It's a triggered ability, so it'll trigger every time a creature dies. If multiple creatures die simultaneously, you choose how to stack the triggers, then get to resolve them one by one.

From the card's Oracle rulings:


  1/1/2011  If multiple nontoken creatures are put into your graveyard
  from the battlefield at the same time, Nim Deathmantle's second
  ability triggers that many times. You put the triggered abilities on
  the stack in any order, so you'll determine in which order they
  resolve. If you pay {4} more than once, each card you paid {4} for
  will end up on the battlefield under your control, and Nim Deathmantle
  will end up attached to the last card that returned to the battlefield
  this way that it could equip.