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The evolution of the traditional nuclear magic numbers away from the valley of stability is an active field of research. Experimental efforts focus on providing key spectroscopic information that will shed light into the structure of exotic nuclei and understanding the driving mechanism behind the shell evolution. In this work, we investigate the spin-orbit shell gap towards the neutron dripline. To do so, we employed (p,2p) quasi-free scattering reactions to measure the proton component of the state of 16,18,20C. The experimental findings support the notion of a moderate reduction of the proton spin-orbit splitting, at variance to recent claims for a prevalent magic number towards the neutron dripline.