  We prove that deformation of F-injectivity holds for local rings
$(R,\mathfrak{m})$ that admit secondary representations of
$H^i_{\mathfrak{m}}(R)$ which are stable under the natural Frobenius action. As
a consequence, F-injectivity deforms when $(R,\mathfrak{m})$ is sequentially
Cohen-Macaulay (or more generally when all the local cohomology modules
$H^i_{\mathfrak{m}}(R)$ have no embedded attached primes). We obtain some
additional cases if $R/\mathfrak{m}$ is perfect or if $R$ is
$\mathbb{N}$-graded.
