We study the two-dimensional extension of the Su-Schrieffer-Heeger model in its higher-order topological insulator phase, which is known to host corner states. Using the separability of the model into a product of one-dimensional Su-Schrieffer-Heeger chains, we analytically describe the eigenmodes, and specifically the zero-energy level, which includes states localized in corners. We then consider networks with disordered hopping coefficients that preserve the chiral (sublattice) symmetry of the model. We show that the corner mode and its localization properties are robust against disorder if the hopping coefficients have a vanishing flux on appropriately defined superplaquettes. We then show how this model with disorder can be realized using an acoustic network of air channels, and confirm the presence and robustness of corner modes.