Here is a very concerning article just published by a practicing physician in Vox. He reports, admittedly on very limited clinical evidence and anecdotal reports from colleagues, that people appear able to get reinfected with COVID after fully clearing an initial infection. He also suggests that such reinfections may be more severe. He compares it to diseases like dengue fever where you get a worse case each time you get it.
We’ve seen a handful of reports like this over the last four or five months. I have generally dismissed them because in every case I had seen (mostly out of East Asia), more thorough analysis showed the reports to be mistaken.