That is a mystery! Assuming you were treated for syphilis the first time and they tested after to make sure it was completely gone? You can have syphilis in the latent phase where you have no symptoms but that would typically be the case if you weren't treated. You tested negative after your initial treatment?
What kind of testing are you having done, and what are the results?
To be considered cured, they look for a 4-fold drop in your titer (e.g., from 1:16 to 1:4 or from 1:8 to 1:32). On some tests, you may always be positive, but it should be a really low number. They should also be using the same tests to compare your results every time you test, and using confirmatory tests.
Do you trust your doctors? Are they specialists?
Yes, your HIV may come into play here. You can read about some special considerations here - https://www.cdc.gov/std/tg2015/syphilis.htm#hiv You can also make sure you were treated correctly, though the treatment regimen is the same.