The Ricci flow is a geometric evolution equation which deforms a Riemannian metric by a multiple of its Ricci curvature. In this talk, we show that if \(g(t)\) is a solution to the Ricci flow satisfying a certain non-uniform curvature bound and \(g(0)\) splits as a product, then the solution splits as a product for all time. The problem is framed as one of uniqueness for a related system to which we apply a maximum principle similar to those used by Huang-Tam and Liu-Szekelyhidi.