I don't think that's the issue. With any virus, your immune system grows countermeasures exponentially (memory t-cells, antibodies, protein complements) to stop it. These stick around after the virus is gone. It's an immune system "memory"

In another infection, your cells still get infected, but the infection is just stopped very quickly. HIV has inscription and reverse transcription enzymes in it, so it can actually glue its sequence into your DNA. It changes your DNA enough to replicate it, but not enough that your cells change their structure so your immune system can't recognize them as infected (and those changes can cause your immune system to fail over time: AIDS).

Even if your body is primed to deal with HIV infections, if the infection happens, it's already too late.

I'm not sure who antiviral drugs like PREP work, but you'd need something like that permanently in your system.