Titration of aspirin
I am afraid, direct acid-base titration is not the right way to analyze aspirin exactly because of the you stated - hydrolysis. The rule number no of any titration is that there should be no side reaction and it should go to completion almost instantly. The direct titration of aspirin is problematic because hydrolyzes pretty fast to salicylic acid- an unwanted side reaction which may or may not go to completion.

In order to circumvent this, analytical chemists do a back-titration. You add an excess of base, heat the mixture so that neutralization as well as hydrolysis are complete. The remaining base is titrated. The rest of the calculations are normally done.