In South Korea, they discovered that all of the many potential reinfections they had detected were due to faulty (overly sensitive) tests. There are no confirmed cases of reinfection and many thousands of people on 'front line' jobs who have recovered form the disease, returned to work and never been reinfected. In a study done on monkeys, scientists were unable to achieve reinfection.

Here is a recent article with some useful links discussing immunity: https://www.sltrib.com/news/2020/05/13/coronavirus-immunity/