The newborn infant cleared the virus from their bloodstream, but HIV re-emerged soon after antiretroviral treatment stopped.
Doctors had hoped rapid treatment would might prevent HIV becoming established in the body.
Experts said there was “still some way to go” before a cure was found.
Drug treatments have come a long way since HIV came to global attention in the 1980s and infection is no longer a death sentence.
However, antiretrovirals merely clear the virus from the bloodstream leaving reservoirs of HIV in other organs untouched.
The hope was that acting before the reservoirs formed would be an effective cure.
Doctors at the University of Milan and the Don Gnocchi Foundation in the city have reported a case, in the Lancet medical journal, of a baby born to a mother with HIV in 2009.
Drug treatment started shortly after birth and the virus rapidly disappeared from the bloodstream. HIV was undetectable at the age of three.
The doctors said: “In view of these results, and recent reports of apparent cure of HIV infection, and in agreement with the mother, we stopped antiretroviral therapy.”
For one week everything seemed fine, but in the second week, after treatment stopped, the virus had returned.
Prof Mario Clerici, from the University of Milan, told the BBC News website: “Just a couple of hours after infection, the virus has already started seeding the organs and hides so therapy cannot eradicate HIV.
“You can treat patients, but you cannot cure them. Right now it is impossible.”
In July, a baby girl in the US born with HIV and believed cured after very early treatment was found to still harbour the virus.
Doctors said tests on the four-year-old child from Mississippi indicated she was no longer in remission.
She had appeared free of HIV as recently as March, without receiving treatment for nearly two years.
“A cure for HIV is still at ground zero,” said Prof Clerici.
Commenting on the findings Prof Sanjaya Senanayake, from the Australian National University Medical School, said: “This case shows that undetectable HIV in the blood does not mean that the body is free from virus and that there is still some way to go before a cure is found.”
Only one person has been “cured” of HIV.
In 2007, Timothy Ray Brown received a bone marrow transplant from a donor with a rare genetic mutation that resists HIV.
He has shown no signs of infection for more than five years.