Thank you for your quick reply. AccountStore does look like the right road to go down, but since this is an OAuth request using Esri's AuthenticationManager, I don't have access to the user's actual username and password. Instead I get back the Credential object, and I'm not sure how I'd store that into AccountStore as that seems to be mostly a key-value store.
I did also check to make sure the credentials we're passing through AddCredential have their ServiceUri set, but it didn't help in persisting through different runs of the app.