Yes, akshar means that which does not fall down, and kshar means that which falls down. The living entity is kshar; that is, prone to fall down into material existence. But the Supreme Brahman is akshar, or does not fall down. The material energy is under the control of the akshar brahman. Another meaning of the akshar brahman is the inhabitants of the spiritual world. They are eternally existing and never fall down. In other words they are called Nitya-Mukti and the kshar brahman is called Nitya Bhadda, or eternally conditioned.
Letter to Sri Shresthaji, 24 April, 1971