Travel at this price begins at the end of August and is valid through February 2019. Travel is available daily, but you'll have the most luck with departures leaving in the middle of the week. A Saturday night stay is required.
As an example, I found seats departing JFK on Wednesday, September 12, and returning from CPT on Wednesday, September 26, 2018.
Need a room in Cape Town? Here's a list of available hotels for the sample dates listed above on Hotelwatchdog.