These NAAT tests have a few issues. The one you are alluding to here is that they are probably only 70-80% sensitive (that is, they will be negative 20-30% of the time when they should be positive). This has more to do with the adequacy of sampling than it does with the the test per se. So it is quite possible to have a false negative test followed by a true positive test a week later. You have been positive throughout, but a test came back false negative as it missed the virus.
This isn't reinfection. This is a function of the performance of the tests when applied to real world collection and processing of samples. With 100's of thousands of people who have been tested, there are going to be countless examples of this pattern.
At the end of the day, this is just a resp virus. A bit more lethal than others, and we don't have any heard immunity to it. So the virus needs to be taken seriously. But it doesn't have magical properties.
It is likely you can only get it once, although it is possible you could get a 2nd (likely milder) case some years later.
And the virus could be unstable (like influenza) that changes each year. But it will be less deadly in future as we will likely retain a degree of heard immunity.