Not really, no. Modern antiretrovirals are exceptionally effective, and for those with access[1] HIV/AIDS has become a chronic illness, with nearly-similar lifespans (due mostly to chronic inflammation).
We still haven't come close to "eradicating" or curing HIV/AIDS; the issue lies in the virus' insidious biology. HIV is a retrovirus, meaning it incorporates into the target cell's genome, specifically CD4+ T-cells. An obvious barrier to "only" 1% of virions is that an infected person produces billions of virus particles every single day[2]. A less obvious barrier is the "latent" reservoir of the virus in cells.
Essentially, not all cells with an incorporated HIV genome are producing virus, and thus these proviruses can evade detection. A 2013 paper in cell[3] provides what I think is the most devastating example of this. Basically, an idea that has gained more traction lately has been to activate these T-cells, thus alerting the immune system and hopefully clearing the virus. It turns out that not all cells are activated, and the size of this reservoir is ~60X larger than previously thought.
When it comes to something like cancer, we often define "cure" or "beating it" differently — look no further than Randall Munroe's heartbreaking visualization, Lanes.[4] We need to do something similar for HIV. We can't get rid of the virus, but we're already pretty good at making life not so bad if you have it. Access and affordability are larger barriers to preventing mortality/morbidity.
There's also a quiet undercurrent that a standard vaccine for HIV is biologically impossible, but that's for another day.
tl;dr HIV sucks but we're okay at managing it. 99% sounds good but it's probably not enough.
1: Read: moderately well-off people with health insurance in wealthy, industrialized nations.
2: DOI: 10.1038/nrg1246 The oft-cited rule of the thumb is that every base of the viral genome is mutated every day.
3: DOI: 10.1016/j.cell.2013.09.020 This one is absolutely worth reading.
4: https://xkcd.com/931