We investigate the steady state of two single-mode, uniform, spatially separated polaritonic condensates exposed to resonant pumping with entangled pairs of photons in the presence of incoherent exciton reservoirs created by non-resonant optical pumping. We demonstrate the principal possibility of driving the system to an entangled state despite its exposure to noises arising from the excitonic reservoirs and photon leakage through the microcavity mirrors. We estimate the minimum pair-induced polariton influx required to drive the system into a steady state that violates the partial-transpose criterion for entanglement. Furthermore, we trace the evolution of the system after a sudden switch-off of the entangled pumping. Our analysis provides estimates for the entanglement lifetime in a system of two exciton-polariton condensates.