ἀΐδιος is from ἀεί, always. It is not built on αἰών. Strong’s glosses it “everduring.” Thayer says eternal or everlasting, and points to αἰώνιος as a synonym discussion. The force is a quality that always holds, not a named age.

The New Testament uses it twice. The two lines belong together: the same adjective names what does not fail in God, and what does not break when God keeps.

In Romans 1:20 it qualifies power: his unfailing power and divinity, clearly seen in what is made. The base text had “everlasting.” That English leans toward endless time. This Bible prints “unfailing,” so the word stays with the reliability of the power, not a clock.

In Jude 1:6 it qualifies bonds: unbreakable bonds under darkness for the judgment of the great day. The Greek is εἰς κρίσιν, for or unto the judgment, not “until.” He has kept them in bonds that hold. The base text had “everlasting.” This Bible prints “unbreakable.”

There is no matching Hebrew lemma behind ἀΐδιος in these verses. The usual Hebrew duration words, including עוֹלָם, answer αἰών and αἰώνιος in the Greek Old Testament. ἀΐδιος is rarer Greek, from “always,” and Wisdom 7:26 uses it in a book written in Greek.