  Let $\omega$ be a Kaehler form on the real $4$-torus $T^4$. Suppose that
$\omega$ satisfies an irrationality condition which can be achieved by an
arbitrarily small perturbation of $\omega$. This note shows that the smoothly
trivial symplectic mapping class group of the one-point symplectic blowup of
$(T^4,\omega)$ is infinitely generated.
