Interestingly I got the problem today after setting up a new project. The previous project worked fine.
I tracked it down, I'm pretty sure, to ProRes media transcoded with Interleaving - I had 1080i 50 field/sec media (which shows up of course as 1080i 25 frames/sec). I had let the media completely transcode and then applied stabilisation and once done absolutely no discernable difference.
I then spotted another thread mentioning that people recognition didn't work on interleaved media so I deleted the clip entirely and re imported it, let it transcode to ProRes and changed the Field Dominance to Progressive prior to stabilising - et voila it worked!
Interestingly the first time I used the stabilisation also worked on media that was still in 1080i but hadn't been transcoded to ProRes because I forgot to check the Import option. This was AVCHD media being stored with a 'H.264, Linear PCM, Timecode' codec.
Anyway, hope that helps somebody until they sort it out.
Oh, almost forgot. There seems to be no way whatsover to make FCPX reanalyse the media once it's done the job. I had to delete the media totally and reimport it to be able to get it working.