Yes, Mormon prophecy has continued to fail and here’s an example.
First remember that in the Old Testament there is a test to determine whether a purported prophet comes from God. In Deuteronomy 18: 21, 22 it says:
And if thou say in thine heart, How shall we know the word which the Lord hath not spoken? When a prophet speaketh in the name of the Lord, if the thing follow not, nor come to pass, that is the thing which the Lord hath not spoken, but the prophet hath spoken it presumptuously: thou shalt not be afraid of him. (KJV–the official Bible translation of the Mormon church)
In Doctrine and Covenants 84 (this is another book the Mormons regard as canonized scripture along with the Old and New Testaments), in 1832, The Lord spoke and said to the church (by Joseph Smith’s revelation):
DC 84: 4-5
4 Verily this is the word of the Lord, that the city New Jerusalem shall be built by the gathering of the saints, beginning at this place, even the place of the temple, which temple shall be reared in this generation.
5 For verily this generation shall not all pass away until an house shall be built unto the Lord, and a cloud shall rest upon it, which cloud shall be even the glory of the Lord, which shall fill the house.
“New Jerusalem” according to Joseph Smith was Independence, Missouri and the place where the temple was to be established there was called the “temple lot”, a small parcel of land about the size of a small city block. However shortly after that revelation was given the governor of Missouri, Lilburn Boggs, issued infamous executive order 44, legalizing the extermination of Mormons in the state and as a result the Mormons fled the area. The long term result was that the parcel of land was never developed (except for a trench that the city later filled) and a temple was never built. To this day if you go to the temple lot in Independence, Missouri, there is nothing more there than an open undeveloped field.
Now, the go-to explanation that a Mormon would/could likely give for this apparent false prophecy in one of their sacred books is that the generation has not run completely out. However, in 1871, thirty-nine years after the revelation was given, the Mormon community was so concerned that this revelation was set to fail the next year that one of the leaders of the church, Orson Pratt (a general authority) said the following:
**He promised us that He would manifest Himself on that temple, that the glory of God should be upon it; and not only upon the temple, but within it, even a cloud by day and a flaming fire by night.
We believe in these promises as much as we believe in any promise ever uttered by the mouth of Jehovah. The Latter-day Saints just as much expect to receive a fulfilment of that promise during the generation that was in existence in 1832 as they expect that the sun will rise and set to-morrow. Why? Because God cannot lie.**
Here, Pratt tried to massage the problem by declaring that anyone alive at the beginning of the generation which everyone assumed was forty years long, would see the temple built at some point in their lives thereby fulfilling the terms of the prophecy.
Apparently God did lie, because as of October 2012, everyone from that generation has long-since died, and no temple stands.
Joseph Smith, the Mormon prophet therefore spoke presumptuously according to Deuteronomy 18, making him a false prophet, and making the Mormon Church a false church.