We study the stability of the classical optimal sequential probability ratio test based on independent identically distributed observations X1,X2,… when testing two simple hypotheses about their common density f: f=f0 versus f=f1. As a functional to be minimized, it is used a weighted sum of the average (under f0) sample number and the two types error probabilities. We prove that the problem is reduced to stopping time optimization for a ratio process generated by X1,X2,… with the density f0. For τ∗ being the corresponding optimal stopping time we consider a situation when this rule is applied for testing between f0 and an alternative f~1, where f~1 is some approximation to f1. An inequality is obtained which gives an upper bound for the expected cost excess, when τ∗ is used instead of the rule τ~∗ optimal for the pair (f0,f~1). The inequality found also estimates the difference between the minimal expected costs for optimal tests corresponding to the pairs (f0,f1) and (f0,f~1).