We study the effect of the exciton fine-structure splitting on the polarisation-entanglement of photon pairs produced by the biexciton cascade in a single quantum dot. The entanglement is found to persist despite separations between the intermediate energy levels of up to 4 micro-eV. Measurements demonstrate that entanglement of the photon pair is robust to the dephasing of the intermediate exciton state responsible for the first order coherence time of either single photon. We present a theoretical framework taking into account the effects of spin-scattering, background light and dephasing. We distinguish between the first-order coherence time, and a parameter which we measure for the first time and define as the cross-coherence time.
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