It's now called Apache River, although I can't make out from that page is it's truly alive. It's not about to take the world by storm, that's for sure. JXTA, on the other hand, appears to be dead in the water.
If I understand correctly, Sun essentially dumped Jini and it was picked up by the Apache project and renamed to Apache River.
It is in 'incubation' there which basically means it is a project in its infancy. I was on the mailing list for a while but there wasn't a lot of movement and most of the discussion was about getting the Apache paperwork filled in each cycle to prevent the project being dropped.
I still see Jini projects from time to time -- although admittedly, they are all from projects that are using Gigaspaces... which makes a JavaSpaces product that can be configured to use the Jini framework.
I haven't seen a single project, in a very long time, that developed applications that directly access the Jini framework.
IMO, it isn't really dead. But I don't think that it can be considered alive either.