Jiji doesn't speak (in human words, at least) to Kiki anymore, because they grew up, not because she lost a power. In the original book, it is explained that a witch girl and a black cat are raised together from infancy, and that's why they can "talk" to each other (notice that Kiki's mom never talks with Jiji directly). They are able to talk to each other because of their close relationship, rather than magic itself (a cat being able to live so long could be magic, though). Miyazaki made Jiji not be able to talk to Kiki even after she regained her power to show that Kiki has grown, and doesn't need her "other self" anymore. Miyazaki says, "The most important thing for Kiki is [...] whether she can meet various people on her own. As long as she is flying on the broom with her cat, she is free. But, to live in a town, to get training means that she has to be able to walk the town alone and talk to people, without her broom or her cat." Kiki and Jiji can start a new relationship as independent personalities. They remain friends, with other meaningful relationships (such as Lily and the kittens for Jiji) added on.
In the Disney dub, Jiji says "Kiki, can you hear me?" before he jumps on Kiki's shoulder, but this line is not in the original.