  It has been recently reported an intriguing theoretical result of a narrow
three-body resonance with a large available phase space. The resonance was
reported in the $N\Lambda\Lambda-\Xi NN$ system near the $\Xi d$ threshold,
having a very small width in spite of the open $N\Lambda\Lambda$ channel lying
around 23 MeV below the $\Xi NN$ channel. We use first-order perturbation
theory as a plausible argument to explain this behavior. We apply our result to
realistic local interactions. Other systems involving several thresholds are
likely to follow the same behavior.
