(T-Detect) I was antibody positive and T-cell negative. Why did this happen?

While no clinical test is 100% sensitive, data showed T-Detect COVID had a sensitivity of 95% at approximately five months after symptom onset. In another study, T-Detect had a sensitivity of 90% at approximately 10 months after symptom onset. Sensitivity is the ability of a test to correctly determine if a person has or had the disease, so 95 out of 100 times T-Detect COVID accurately determined if someone had the disease. 

That said, it is unclear exactly how long T cells remain after a COVID-19 infection. Therefore, it is possible to have had COVID-19 and for T cells to have diminished by the time of testing to a number that is not detectable by laboratory tests.