New measurements of fusion cross sections at deep sub-barrier energies for the reactions 16O+{204,208}Pb show a steep but almost saturated logarithmic slope, unlike 64Ni-induced reactions. Coupled channels calculations cannot simultaneously reproduce these new data and above-barrier cross-sections with the same Woods-Saxon nuclear potential. It is argued that this highlights an inadequacy of the coherent coupled channels approach. It is proposed that a new approach explicitly including gradual decoherence is needed to allow a consistent description of nuclear fusion.