Adiabatic rapid passage (ARP) is demonstrated in a single In(Ga)As quantum dot (QD) over a wide range of laser tuning relative to the exciton transition energy to assess the level of robustness of this quantum state inversion gate for practical QD systems. Our experiments indicate a drop in exciton inversion by only 5% for a detuning of 9.3 meV, indicating accessible detunings that span the typical inhomogeneous broadening of self-assembled QD ensembles. Our findings indicate that ARP is an ideal control protocol for synchronous triggering of quantum light sources for applications in photonic quantum technology.