Above-barrier fusion cross-sections for an isotopic chain of oxygen isotopes with A=16-19 incident on a $^{12}$C target are presented. Experimental data are compared with both static and dynamical microscopic calculations. These calculations are unable to explain the $sim$37% increase in the average above-barrier fusion cross-section observed for $^{19}$O as compared to $beta$-stable oxygen isotopes. This result suggests that for neutron-rich nuclei existing time-dependent Hartree-Fock calculations underpredict the role of dynamics at near-barrier energies. High-quality measurement of above-barrier fusion for an isotopic chain of increasingly neutron-rich nuclei provides an effective means to probe this fusion dynamics.