Aidios was used as a time word, I don’t agree with this explanation, however it was used sometimes in a more limited sense too as has been argued by some universalist scholars, I was able to confirm this quote:
The Peloponnesian War, Book 6, chapter 24, section 3, can be find here:
All alike fell in love with the enterprise. The older men thought that they would either subdue
the places against which they were to sail, or at all events, with so large a force, meet with no
disaster; those in the prime of life felt a longing for foreign sights and spectacles, and had no
doubt that they should come safe home again; while the idea of the common people and the
soldiery was to earn wages at the moment, and make conquests that would supply a neverending fund of pay [aidion misthophoran] for the future.
The context suggests that it didn’t meant literally everlasting there, a commentary states: “aidion misthophoran - this is explained by editors to mean that the addition of Sicily to the empire would lead to continual campaigns; but Gilbert rightly paraphrases: ‘they hoped to get permanent employment out of the acquisition somehow’: misthophora is used loosely for pay for any services.”