I decided that this might merit a thread after seeing this article, which suggests based on the small size of the optic lobe that elephant birds were probably nocturnal or at least crepuscular.
There are fairly few nocturnal birds, and they are usually nocturnal to pursue nocturnal food sources, such as owls and nightjars. A few are nocturnal to avoid predators (many only during nesting season), but that seems unlikely for the elephant bird. Given that the elephant bird's diet probably consisted of fruit, there doesn't seem to be much reason for it to be nocturnal to find food either.
One possibility: its closest relative is the kiwi, which is also nocturnal. Maybe the ancestor of both birds was nocturnal, and there was no pressure on the elephant bird to resume diurnal habits.