We're leaving MSY on 5/17.
When the fares were first released, they were $124 each way. Within a couple of weeks, they went down to $94 each way, so I went ahead and booked.
Since then, I've been checking back periodically, and they haven't moved. Once, when I just happened to check back, there were special Internet Fares listed for $59 each way, but they were (of course) booked. This wasn't a ding, so I'm thinking it was just the luck of the draw.