Super-entropic black holes possess finite-area but noncompact event horizons and violate the reverse iso-perimetric inequality.It has been conjectured that such black holes always have negative specific heat at constant volume CV or negative specific heat at constant pressure Cp whenever CV ＞ 0,making them unstable in extended thermodynamics.In this paper,we describe a test of this instability conjecture with a family of nonlinear electro-dynamic black holes,namely 3D Einstein-Born-Infeld (EBI) AdS black holes.Our results show that when nonlinear electrodynamics effects are weak,the instability conjecture is valid.However,the conjecture can be violated in some parameter region when nonlinear electrodynamics effects are strong enough.This observation thus provides a counter example to the instability conjecture,which suggests that super-entropic black holes may be thermodynamically stable.