Newtonian physics can help illustrate this. If a rocket has enough thrust to achieve escape velocity, then off it goes to the depths of space. Or maybe it's slower and just achieves a stable orbit. Or too slow and crashes into the ground.
In this metaphor, the rocket, which is the forked project, will take energy from the parent project. If it doesn't get enough energy (in the form of talent, community passion, motivation, etc.), the child may fail. Or, as in the case with so many Linux distros, achieve a nice stable orbit with the upstream parent.
It may come down to timing. If history were the only factor here, it would seem LibreOffice and The Document Foundation have enough energy, momentum, and passion to suck the life out of OpenOffice.org and bring it to an end, if OpenOffice.org does not have a chance to recover fast enough. That may still happen, particularly if OpenOffice.org and its sponsors can't tap into the energy of the marketplace in time. In this scenario, it's OpenOffice.org that should be worried about resources, not LibreOffice.