The potential energy between the O atoms in the H bond has the form of an anharmonic potential an example of the shape is the Morse potential or a Lennard-Jones 6-12. The energy is zero at large O-O separation and moves to a minimum as this distance is reduced (the point at which a the H bond exists with the H atom between the two O atoms, typically 0.15-0.25 nm). As the O-O distance is further reduced the potential rises again to zero then positive potential energy. The H bond thus forms in a lop-sided potential well, with the H atoms between the two O atoms. (I imagine the effect on the covalent bonds would be less as they are stronger and shorter than the H bond.)
Suppose that the distance between the O-O atoms is reduced then the potential rises and becomes closer to zero or repulsive (positive) potential. Suppose that the pressure causes this to happen just a little and is such that the H bond energy is now only slightly below zero. At this point the thermal energy (as molecular vibrations) could in places be enough to increase the energy above zero and so break the H bond, at which point the solid would start to melt. The structure beginning to break down could further collapse rather like a building collapses by bending and twisting if it structural girders are removed.