Odd as it may seem, the reason rails are still in place at Gato on the Southern Ute Reservation is the fact that the tribe asserted its rights under the "Indian Non-Intercourse Act of 1790." This law, which Congress enacted in the early days of our national history, holds that non-Indian entities
cannot purchase or lease property from Indian Nations without the express authority of Congress. In the past, states and various private companies elected to "forget" about that statute in the era when tribes weren't all that familiar with their rights and/or lacked the power to insist that whites follow the law of the nation. But that was then, and this is now.
Nothing in this says sovereign tribal governments can prevent an operating railroad from crossing their territory- even if that railroad failed to get Washington's blessing for their lease. Stopping operations would constitute "adverse abandonment" -- and the "Great White Chief" in Washington pre-empts the power of what the Supreme Court holds are "domestic dependent nations." (Only the ICC or its successor, the Surface Transportation Board, may authorize the abandonment of common-carrier railroad lines.)
However, when a route like the San Juan Extension is formally abandoned, tribes with sovereignty over the land it once crossed may assert ownership to all "additions and betterments" the railroad made to its leasehold. In that event, the railroad is in a weak legal position if it never received Congressional ratification of its lease arrangements in the first place and, even if that authority was given, the lease failed to specify what happens to the improvements after it is terminated.
I'm familiar with situations where an Indian nation successfully asserted ownership to
all of the rail and OTM
following an abandonment. While I don't know details about Gato, I suspect that the DRGW may have encountered this issue when scrappers attempted to remove rail and fittings on line across the Southern Ute Reservation. They may have decided to leave things where they were -- letting the Utes have title to the scrap.