One what basis do you judge "holding fast" by, professions or practice? Yea, a man may say, Thou hast faith, and I have works: shew me thy faith without thy works, and I will shew thee my faith by my works. (James 2:18)
And what is the basis for your assurance that Rome is holding fast to the doctrine it received from the Apostles? The weight of Scripture or the statements of your church that she is doing so?
Because Jesus promised the Apostles the Holy Spirit would guide His Church and that evil would not prevail over it. I believe Him. His Church may grow smaller; but the faithful will still be doing things the way Christ wanted it done, guided by the Third Person of the Trinity. Christ’s Church will continue to be unified; it will continue to be holy; it will continue to be for anyone; it will continue to be faithful to the doctrines taught by the unbroken succession of Apostles. Just as He told us.
He doesn’t like the lukewarm anyway, so they are a small loss.