How can Nirvana (Nibbana) be permanent? If everything is impermanent and this is used as a reason why Buddhists do not believe in a creator and eternal God, how can Nirvana be permanent?

Did the Buddha ever explain this point?
There is a famous set of verses of the Buddha that go as follows:


  
  “All conditioned things are impermanent” – when
  one sees this with wisdom, one turns away from
  suffering. This is the path to purification.
  “All conditioned things are unsatisfactory” –
  when one sees this with wisdom, one turns away
  from suffering. This is the path to purification.
  “All things are not-self” – when one sees this
  with wisdom, one turns away from suffering.
  This is the path to purification.
  
  
  -- Dhp. 277-9 (Buddharakkhita, trans)


Do you see the difference?

Nowhere did the Buddha say that everything is impermanent, because it is not true. All things that arise must cease (SN 56.11), and that is the key to answering this question, because nibbaana is unarisen:


  And what is the noble search? Here someone being himself subject to birth, having understood the danger in what is subject to birth, seeks the unborn supreme security from bondage, Nibbāna;
  
  -- MN 26 (Bodhi, trans.)


The logical conclusion of not being born is not dying, and so:


  being himself subject to death, having understood the danger in what is subject to death, he seeks the deathless supreme security from bondage, Nibbāna;
  
  -- Ibid