This meta analysis only includes studies of multi patients so there's pretty much a guarantee that there are individual case studies that differ from this.
The paper cites 34 replication cycles as the lower bound to obtain viable viral cultures. Whether a PCR test is reported as "positive" depends on the chosen replication cycle threshold (Ct value). As far as I'm aware, this "magic number" is usually chosen to be 35.
Beyond that, it is possible to do more cycles to demonstrate the existence of trace amounts of PCR fragments, but such a test would not be considered "PCR positive".
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.
That does put into question the validity of counting PCR test positives as a benchmark of viral load among the population, but as a safety measure for potentially infected individuals, the trade-off is worthwhile.