While plasma-based accelerators have the potential to positively impact a broad range of research topics, a route to application will only be possible through improved understanding of their stability. We present experimental results of a laser wakefield accelerator in the nonlinear regime in a helium gas jet target with a density transition produced by a razor blade in the flow. Modifications to the target setup are correlated with variations in the plasma density profile diagnosed via interferometry and the shot-to-shot variations of the density profile for nominally equal conditions are characterized. Through an in-depth sensitivity study using particle-in-cell simulations, the effects of changes in the plasma density profile on the accelerated electron beams are investigated. The results suggest that blade motion is more detrimental to stability than gas pressure fluctuations, and that early focusing of the laser may reduce the deleterious effects of such density fluctuations.