Synonyms for Never-ending:

adj.

continual, unceasing (adjective)
amaranthine, continuous, uninterrupted, constant, persistent, perpetual, ceaseless, unremitting, incessant.
timeless (adjective)
regular, persistent.

adv

continuously (adverb)
on and on.

n.

extended, on and on, long-term, enduring, prolonged, long, for some time, lasting. world without end, Eterne, amaranthine, continue. never-ending (noun)
constant, uninterrupted, perpetual, ceaseless, unceasing, incessant, unremitting, continuous.

Other synonyms:

enduring, extended, world without end, amaranthine, lasting, prolonged. Eterne, long-term. long. Other relevant words:
enduring, lasting, Eterne, on and on, extended, regular, amaranthine, continue, long-term, persistent, long, prolonged.