The main purpose of this clinical study is to see if a maintenance dose of GEN-003 reduces the number of days that subjects have a genital herpes recurrence. Other purposes of the study are to 1) see how safe and tolerable a maintenance dose is, and 2) to see if a maintenance dose of GEN-003 reduces the number of days that the herpes simplex virus type 2 (HSV-2) is found in the genital area (viral shedding).