I've been wrestling with this whole "reinfection" idea. Unless the virus is doing something really screwy to peoples immune systems (and it might be, at least in some cases), it just doesn't seem likely that people are getting reinfected a couple of weeks after the first infection. That's just not how most viruses work.
I think it's more likely that these cases are reflective of testing issues. The PCR tests seem to be somewhat "flaky" for lack of a better term. There have been numerous cases reported from China where people were obviously symptomatic (fever, cough) and even with ct manifestation of pneumonia, who repeatedly tested negative before finally getting a positive result. So I bet most of these "reinfection" cases are due to the nature of testing - the people still have virus in their systems but the tests come back negative. Then later they get a positive test - not because they were reinfected but because they never got rid of all the virus.
Another possibility is that there is residual viral RNA in the system and the tests sometimes pick it up, and sometimes don't. These people may or may not still be contagious and that needs to be figured out obviously. From what I've read there are other viral infections where people can still test positive for a long time but are not actually infected or shedding virus.
If it turns out that true reinfection is common then we are in big trouble. I'd rather not contemplate that scenario.