I'd bet on AUFS - I noticed that the disappearance is being triggered by deletion of the corresponding (empty!) dirs from /initrd/pup_rw/initrd/.
So, restricting to max. second level (rmdir */*) would prevent that.
But why's that happening? No idea, ask Junjiro R. Okajima. ;)
BTW, in PUPMODE=13 /initrd/pup_rw/initrd/ contains only tmp dir.