Around half of all people taking an antidepressant have "treatment-resistant depression" (TRD), which means the drug does not help their condition. But there is a smaller minority who develop "chronic depressive syndrome" - which means their depression worsens - as a direct consequence of taking an antidepressant, such as Prozac.
Researchers from the Louisville School of Medicine call the drug-induced depression "tardive dysphoria", mirroring tardive dyskinesia, which is caused by antipsychotic drugs. Tardive dysphoria is "an active process in which a depressive picture is caused by continued administration of the antidepressant."
(Source: Medical Hypotheses, 2011; 76: 769-73).