"εις το διηνεκές" (prepositional time definition) = for ever, eternally
διηνεκής (adjective) = something that lasts for ever, without ever stopping.
continuously (adverb) = constantly, without interruption.
continually = very often, at regular or frequent intervals.
So the initial translation you gave seems more correct:
"because by one sacrifice he has made perfect forever those who are being made holy."
I don't think it makes sense to replace "διηνεκές" with either "continuously" or "continually", because you are not taking into account the "εις το".