The accoustic sum rule correction corrects the non-zero accoustic frequencies at the gamma point. However, your gamma point frequencies are all zero. The negative bulge appears at finite wavevectors.
Assuming that it is not a numerical effect, and you have optimized your forces sufficiently, there is still the chance that the structure is not in a minimum but at a saddle point, e.g. stabilized by the symmetry.
In this case further optimization does not help, but you might try and rattle the atoms a bit to break the symmetry and then optimize again. If the resulting structure is different from the original structure, then this might be the origin for the negative frequencies.
Moreover, although it is generally possible to calculate phonon frequencies for strained systems, a compressed cell sometimes enhances such effects (see e.g. the tutorial
http://www.quantumwise.com/documents/tutorials/latest/Phonon/index.html), especially for lower dimensional systems, such as graphene, which tends to buckle if you compress the cell. In this case, optimizing the cell can help to remove negative frequencies (I don't know if you already tried optimizing your cell).
Finally, be aware that you optimize the small cell, whereas the actual phonon calculations are carried out in the repeated supercell. If you have instabilities that occur at a larger scale, they may be stabilized by the periodicity of the small cell. A good example for such behaviour is again the graphene sheet that tends to buckle (e.g. because you compress the cell). You won't see the buckling in the small cell, because the wavelength of the buckling is larger than the cell length, but in the repeated supercell, the buckling may well be possible.
It don't know if any of these causes apply to your system, but it is something to think about when you encounter negative phonon frequencies.
