Earlier quoted context omitted.
The CDC recently admitted as much. People can test positive for covid weeks after initially testing positive. Which implies they still are shedding the virus. https://twitter.com/abc/status/1476189028982702080?s=21
This happened to me. I tested positive a month after infection (was testing once or twice a week). I isolated anyways to be safe
Apparently PCR tests and antigen tests differ in this regard, but RIP to our insurance providers paying for millions of redundant tests