Thing is that you wouldn't expect many people to have had it twice... yet.
If the antibodies last about 6 months, then people would only have been able to catch it again since September.
And a relatively small proportion of people were tested in March, so a fair number who may have had it twice, won't know for certain.
Certainly at one point they only considered it twice if they could confirm that the structure of the virus was different-and they don't check the structure of most positives.
Up to the end of June there were only 316184 positive tests-that's approximately 0.5% of the population, and they're the only ones who could test positive twice if immunity lasts only 6 months.
I think on that basis that reinfection is very unlikely currently, so you wouldn't expect to see many reinfections.
However the new variant seems to have a higher rate of reinfection than we've seen before, Whether that's because they can say this variant wasn't about back when they had their first positive test, or because immunity is wearing off from the first set of people who had it, or because it has mutated enough (like flu does) for reinfection, I will leave up to the scientists to investigate.
The reason for not testing again within 3 months, I thought was because you will continue to test positive for some time afterwards as the virus will still be there.