We prove stability of shape resonances for the sequence of Schrödinger equations ( − d 2 / d x 2 + U ( x ) + W n ( x ) ) ψ ( x ) = E ψ ( x ) , 0 ⩽ x > ∞ ( - {d^2}/d{x^2} + U(x) + {W_n}(x))\psi (x) = E\psi (x),0 \leqslant x\, > \infty , in the limit n → ∞ n \to \infty where the barrier potentials W n ( x ) {W_n}(x) are integrable, nonnegative, supported in the interval [ 1 , a ] ( 1 > a > ∞ ) [1,a]\;(1 > a > \infty ) , and approach infinity pointwise a.e. for x ∈ [ 1 , a ] x \in [1,a] as n → ∞ n \to \infty . In the course of our investigation we prove that for suitable complex initial conditions the solution to the Riccati equation S ′ ( x ) = 1 − ( W n ( x ) − E ) [ S ( x ) ] 2 S’(x) = 1 - ({W_n}(x) - E){[S(x)]^2} goes to 0 0 as n → ∞ n \to \infty uniformly on compact subsets of [ 1 , a ] [1,a] . Our approach is via ordinary differential equations using outgoing wave boundary conditions to define resonances. Our stability result extends a similar result of Ashbaugh and Harrell, who use an argument based on asymptotics and the implicit function theorem to study the above problem with λ V ( x ) \lambda V(x) replacing W n ( x ) {W_n}(x) . Our approach is to use the Riccati equation analysis mentioned above and an application of Hurwitz’s Theorem from complex variable theory.