Authors’ abstract: Let \(X\) be a complex Banach space, \(N\) a norming set for \(X\), and \(D\subset X\) a bounded, closed, and convex domain such that its norm closure \(\overline D\) is compact in \(\sigma(X,N)\). Let \(\emptyset\neq C \subset D\) lie strictly inside \(D\). We study convergence properties of infinite products of those self-mappings of \(C\) which can be extended to holomorphic self-mappings of \(D\). Endowing the space of sequences of such mappings with an appropriate metric, we show that the subset consisting of all sequences with divergent infinite products is \(\sigma\)-porous.