This very recent (and freely available) review pretty much sums the problem up in the introduction:
http://dx.doi.org/10.1038/clpt.2012.202 (Barton et al., 2013: Prospects for Treatment of Latent HIV)
And here's an update more specifically on the problems with actually curing an individual of HIV infection, if you have access: http://dx.doi.org/10.1016/S0140-6736(13)60104-X (Katlama et al., 2013: Barriers to a cure for HIV: new ways to target and eradicate HIV-1 reservoirs)
Essentially, current antiretroviral therapy (ART) is able to nearly fully suppress active HIV, practically restoring the individual to a healthy status, including the prevention of transmission from them. However, the therapy needs full adherence (missing a dose can already cause viral loads to rise) and is lifelong. The reason for this is because HIV integrates into the genome of host CD4+ T cells, of which there are latent populations in places difficult to reach with therapeutics such as peripheral lymph nodes.
Apparently, some rare individuals actually achieve a "functional cure", i.e. the body is able to suppress viral replication for a given period of time (5 years) without ART. But these patients "are characterised by a favourable HLA profile and potent HIV-specific CD8 T-cell responses that are associated with a low viral DNA reservoir" (Katlama et al). They also mention another group of five patients who did not seem to have a favourable genetic profile and were still able to control HIV following cessation of ART for several years (http://dx.doi.org/10.1097/QAD.0b013e32833b61ba Hocqueloux, 2010: Long-term immunovirologic control following antiretroviral therapy interruption in patients treated at the time of primary HIV-1 infection). So it seems there are plenty reports of people who are able to remain free of detectable viral loads and maintain CD4+ T cell counts for a long time after treatment, but it doesn't seem like any of them stay permanently virus-free.