Solved: if it may help someone else, it appeared that the CHMOD of the wp-content/buddypress folder had been set to 0755 at some point (I had just migrated my whole install, that’s probably when it happened). Resetting to 0775 did the trick.
Update: I have re-run the automatic update, just to make sure – and it successfully completed so I’m pretty sure I’m on 1.5.3.1. However the upgrade notification won’t go away… Anyone?
