Mathematical truth may evolve
Iintuitionism holds that mathematical truth evolves. If so, there's no reason to believe that the Gödel sentence generated by system will still be that system's own Gödel sentence when the sentence is later evaluated.
Penrose assumes that all mathematicians agree on a shared and immutable notion of mathematical truth. But a major school of mathematics, intuitionism, holds that mathematical truth involves is instead.
Jon Doyle (1990).