It's currently unknown if there is an immunity after getting Corona.
Francois Balloux (Computational biologist, director of UGI at UCL): "How long immunity lasts for following covid-19 infection is the biggest unknown. Comparison with other Coronaviridae suggests it may be relatively short-lived (i.e. months). If this were to be confirmed, it would add to the challenge of managing the pandemic.
https://twitter.com/BallouxFrancois/status/12388371671426416...
It's not inconsistent per say, since it still seems that the recent reinfections were likely due to test error or rare poor immune response, but my initial comment is misleading enough that I retract it (and would delete it if I could).