Mosiah 3

As king Benjamin relates the things that an angel told him in the night concerning the coming of Jesus Christ and his atonement, he teaches -

"...behold, and also his blood atoneth for the sins of those who have fallen by the transgression of Adam, who have died not knowing the will of God concerning them, or who have ignorantly sinned."  (Book of Mormon | Mosiah 3:11)

But then he adds -

"But wo, wo unto him who knoweth that he rebelleth against God! For salvation cometh to none such except it be through repentance and faith on the Lord Jesus Christ."  (Book of Mormon | Mosiah 3:12)

At first one may think that it may be better not to know that know.  These two verses also led my thoughts to the baptism of children where in multiple places it is declared -

"...little children need no repentance, neither baptism. Behold, baptism is unto repentance to the fulfilling the commandments unto the remission of sins.
12 But little children are alive in Christ, even from the foundation of the world..."  (Book of Mormon | Moroni 8:11 - 12)

For -

"...all children who die before they arrive at the years of accountability are saved in the celestial kingdom of heaven."  (Doctrine and Covenants | Section 137:10)

Also knowing -

"...chosen messengers went forth to declare the acceptable day of the Lord and proclaim liberty to the captives who were bound, even unto all who would repent of their sins and receive the gospel."  (Doctrine and Covenants | Section 138:31)

And -

"The dead who repent will be redeemed, through obedience to the ordinances of the house of God..."  (Doctrine and Covenants | Section 138:58)

I may be going out on a limb here but even though children are saved in the kingdom of God with no baptism as well as the ignorant are not held responsible, all because of the atonement of Jesus Christ, I also realize that there is an eternal law of agency.  This would suggest to me that under any condition if anyone used their agency in any act of sin or rebellion, that cannot be saved "except it be through repentance and faith in the Lord Jesus Christ". 

In my mind, this would suggest that our love to those we have a relationship with (sealed or family), we would always work to teach our children repentance and faith in the Savior.  It would seem to me an eternal effort.