The issue is that a PCR test does not actually tell us if a virus particle is live or inactive. A shed virus particle can still have intact RNA for the region tested by PCR.

There are published case reports where someone has tested PCR positive during an infection, then PCR negative, and then PCR positive again later and the explanation given has been that they did not get re-infected and their infection did not flare back up but just that virus had been continually shed and the later test was able to capture that.

edit: s/DNA/RNA. The PCR process actually operates on DNA so the virus RNA is converted to DNA as the first step of RT-PCR.