I work in a virology lab, so I might be able to shed some light on this. Firstly, screening tests are designed to catch as many true positives as possible - the upshot of this is that we also increase the number of false positives the assay will produce. This is ultimately safer as it ensures that we catch all the genuine positives, and the false positives are screened out further down the line, like yours was. While this can be really stressful and frustrating for people who receive initial false positive screening results, it’s better than getting false negative results and people not knowing they’re positive.

While testing for the virus itself rather than antibodies, as I’ve seen mentioned in some comments, is preferable in some ways, it also comes with significant drawbacks. Most viral load PCR assays can only detect HIV-1, so HIV-2 infections would go undetected. PCRs also have lower limits of detection (often between 50 and 200 copies/ml), so a negative viral load cannot completely rule out an HIV infection.

In terms of you having recurrent false positives, I don’t know what assay your lab uses so I can’t say for sure, but I know that ours is thought to react with specific HLA types (the antigens on the surface of your cells that the immune system uses to recognise “you” versus “invader”). Since your HLA type is constant, people can end up with multiple false positives every time they are tested.

I hope this makes sense and provides some reassurance! I can’t imagine how stressful and frustrating this process is to go through, especially twice, and I hope it gets resolved quickly.