In one embodiment, a point of local repair (PLR) for a child tunnel establishes a backup tunnel to a hierarchical tunnel head-end node's (grooming node's) downstream hierarchical tunnel neighbor (merge point) and learns a corresponding backup tunnel label. The PLR then stores a label stack having at least i) the backup tunnel label, ii) a hierarchical tunnel label for the merge point, and iii) a child tunnel label as advertised by an hierarchical tunnel tail-end node. Upon failure of the grooming node, the PLR pushes the stored label stack onto traffic for the child tunnel, and reroutes the traffic with the pushed label stack onto the backup tunnel toward the merge point (e.g., so the merge point may receive the traffic with a proper/expected label stack).