I gave up trying after the last conversation, but I have a similar experience.
After installing the portable/patch, mentioned above, I was happy to see that the first CD I played got scrobbled properly. But on either the next CD or the next start of the app, was back on square one.
I also tried logging out/back in and it indeed helped a few times, now it doesn't help either.
BTW, I'm not skipping tracks, but listening to entire albums. And last.fm login/connection seems to be fine, as the currently played song is showing up as "Scrobbling now" in last.fm, it just never gets recorded/into history when the next track begins.