let $a$ denote a non-constant ordinary abelian surface over a global function field (of characteristic $p > 2$) with good reduction everywhere. suppose that $a$ does not have real multiplication by any real quadratic field with discriminant a multiple of $p$. then we prove that there are infinitely many places modulo which $a$ is isogenous to the product of two elliptic curves. this is joint work with davesh maulik and yunqing tang.