There are at least two Book of Mormon passages that imply a restoration of the Church and a continuance of the Church until the second coming.
1 Nephi 14:12-14–Nephi sees in vision the “church of the Lamb of God” in the last days. Although “its numbers were few,” “the saints of God, were also upon all the face of the earth.” In time “the power of the Lamb of God…descend[s] upon the saints of the church of the Lamb, and upon the covenant people of the lord, who [are] scattered upon all the face of the earth; and they [are] armed with righteousness and with the power of God in great glory.” Subsequently he sees the destruction of the wicked in preparation for the Second Coming.
Jacob 5:70-72, 75–Zenos sees that before “the end cometh” the Lord of the vineyard sends “his servant” down who “brought other servants; and they were few. And the Lord of the vineyard said unto them: Go to, and labor in the vineyard, with your might. For behold, this is the last time that I shall nourish my vineyard; for the end is nigh at hand, and the season speedily cometh; and if ye labor with your might with me ye shall have joy in the fruit which I shall lay up unto myself against the time which will soon come. And it came to pass that the servants did go and labor with their mights; and the Lord of the vineyard labored also with them; and they did obey the commandments of the Lord of the vineyard in all things...And it came to pass that when the Lord of the vineyard saw that his fruit was good, and that his vineyard was no more corrupt, he called up his servants, and said unto them: Behold, for this last time have we nourished my vineyard; and thou beholdest that I have done according to my will...”
I think this passage is clearly speaking of what started in 1820 and continues until this day. God sent his servant and a few others with him and he has been nourishing his vineyard for the last time in preparation for “the end” which “is nigh.” His servants are “obey[ing] the commandments of the Lord of the vineyard in all things” and He is “do[ing] according to [his] will.” He is laboring with them. Does this mean that his servants can’t occasionally miss a branch that should be pruned or a weed that should be pulled? Or, on the other hand, that sometimes a branch is loped off that shouldn’t be? I don’t think we can expect that kind of perfection out of humans, but they are doing a good job taking care of the vineyard and preparing it for the harvest which is soon to come.
There is another interesting scripture found in the Doctrine and Covenants regarding the kingdom of God. Section 65 should be read in its entirety, but verse 2 is particularly meaningful in this context: “The keys of the kingdom of God are committed unto man on the earth, and from thence shall the gospel roll forth unto the ends of the earth, as the stone which is cut out of the mountain without hands shall roll forth, until it has filled the whole earth.” This should be compared to Joseph Smith’s bold statement commonly called “the Standard of Truth:”
“[T]he Standard of Truth has been erected; no unhallowed hand can stop the work from progressing; persecutions may rage, mobs may combine, armies may assemble, calumny may defame, but the truth of God will go forth boldly, nobly, and independent, till it has penetrated every continent, visited every clime, swept every country, and sounded in every ear; till the purposes of God shall be accomplished, and the Great Jehovah shall say the work is done.”
Yes, the Church is still true. Yes, it will continue to be so until the work is done and Christ reigns personally on the earth.