  We prove that the bi-invariant Einstein metric on $SU_{2n+1}$ is isolated in
the moduli space of Einstein metrics, even though it admits infinitesimal
deformations. This gives a non-K\"ahler, non-product example of this phenomenon
adding to the famous example of $\mathbb{CP}^{2n}\times\mathbb{CP}^{1}$ found
by Koiso. We apply our methods to derive similar solitonic rigidity results for
the K\"ahler--Einstein metrics on `odd' Grassmannians. We also make explicit a
connection between non-integrable deformations and the dynamical instability of
metrics under Ricci flow.
