From what I've read, the issue is not so much the killing of neurons, as much as the pruning of the neural spines. This dendritic atrophy results in fewer connections with neighbouring cells, and a less organised network of cells which interferes with brain function.

Some articles:
RECENT ADVANCES IN THE NEUROBIOLOGY OF SCHIZOPHRENIA
Prefrontal cortical dendritic spine pathology in schizophrenia and bipolar disorder. - PubMed - NCBI
Dendritic atrophy :: DNA Learning Center

It seems the condition is associated with sustained stress in depression, bipolar disorder and schizophrenia and who knows what else.