Structured solid targets are widely investigated to increase the energy absorption of high-power laser pulses so as to achieve efficient ion acceleration. Here we report the first experimental study of the maximum energy of proton beams accelerated from sub-micrometric foils perforated with holes of nanometric size. By showing the lack of energy enhancement in comparison to standard flat foils, our results suggest that the high contrast routinely achieved with a double plasma mirror does not prevent damaging of the nanostructures prior to the main interaction. Particle-in-cell simulations support that even a short scale length plasma, formed in the last hundreds of femtoseconds before the peak of an ultrashort laser pulse, fills the holes and hinders enhanced electron heating. Our findings reinforce the need for improved laser contrast, as well as for accurate control and diagnostics of on-target plasma formation.