Kittens born to an FIV mother will inherit her antibodies, but not usually the virus.
A mother cat with FIV will have FIV antibodies which are produced by her immune system in response to the virus.
When pregnant, she will pass these antibodies to her kittens through the blood, but she will not pass the virus, which will not cross the placenta.
Because the test for FIV actually looks for the antibodies and not the virus, a kitten from an FIV mother will show positive on the test without any virus being present.
As the kittens grow, they will gradually lose their inherited protection, and will then test negative. This can take several months, the actual time varies between kittens, so any FIV positive test is not safe until the kitten is at least six months old, and possibly older.
Kittens who really are FIV, are not common. The virus is present in the milk, and yet it is rare that the kittens actually get the virus from their mother (this also shows how hard it is to transmit the virus across the mucous membrane, indicating that the virus is not at all contageous).
We recently were in contact with a rescue group who rescued 18 kittens from a farm colony - all kittens tested positive for FIV. Later, the group tested them again with a PCR test (which actually tests for the dna of the virus itself) which showed that of the 18, only one was actually infected with the virus.
If a kitten really is FIV, then it is thought that their life may be shorter than most because they were infected before their immune system was developed. However, we have heard of FIV kittens that have not picked up general sniffles and runny eyes when their non-FIV siblings have done so, so we are not sure just how they are affected.