If Chesterton's fence is intangible and invisible, then it's appropriate to remove it entirely. If it doesn't have a working latch, it doesn't serve as a hard barrier, but it may still serve as a soft barrier, and that may be good enough.

Or, conversely, important things may have been relying on access via the latch-free fence gate: fixing the latch without providing a more appropriate solution to those issues could cause more harm than the benefit you get from "now the fence actually functions as a barrier". (Sure, the latch keeps the wolves out, and stops them picking off the sheep – but it also keeps the sheep away from their only freshwater source, without which most of the sheep are going to die.)