A technique dynamically protects against failure of a head-end node of one or more primary Traffic Engineering Label Switched Paths (TE-LSPs) in a computer network. According to the novel technique, a neighboring upstream node (“protecting node”) of the head-end node learns of the primary TE-LSPs (and their respective state control blocks) extending from the head-end node to one or more address prefixes. The protecting node establishes a repair TE-LSP for each of the primary TE-LSPs to a corresponding downstream neighboring node of the head-end node (a “next-next-hop”). In response to detecting a failure of the head-end node, the protecting node locally reroutes traffic destined for the address prefixes to an appropriate repair TE-LSP. Due to the failure of the head-end node, the protecting node then refreshes the states of the primary TE-LSPs using replicated state control blocks accordingly, until the repair TE-LSPs are no longer needed.