In the case of the Matter of Zamora, 17 I&N Dec. 395 (BIA 1980) [PDF version], if an LPR parent is ruled to have abandoned his/her LPR status while abroad, then the child of the LPR will also be considered to have abandoned his LPR application.
In a similar case, the Matter of Winkens, 15 I&N Dec. 451 (BIA 1975) [PDF version], a 14-year-old child lost his LPR status – when his parents abandoned their US residence and the child left in the custody of the parents.
In other cases, the abandonment cases confirm that the status of an LPR child is dependent on the status of the LPR parent.
In a Ninth Circuit Court case, In Khoshfham v. Holder, 655 F.3d 1147 (9th Cir. 2011) [PDF version], the Court did find a distinction. The court ruled that the abandonment carry-over to the child only applies if the abandonment occurs before the child turns 18. If a child is 18 or older when his/her parent abandons their LPR status, that abandonment will not apply to the child. A separate determination must be made regarding the intent of the child separate from the intent of the parent.