2. Open an org-file containing the following entry.

--8<---------------cut here---------------start------------->8---
* TODO Repeating task
  SCHEDULED: <2014-03-02 Sun .+2w>
  :LOGBOOK:
  - State "DONE"       from "NOW"        [2014-02-23 Sun 08:39]
  CLOCK: [2014-02-23 Sun 08:26]--[2014-02-23 Sun 08:39] =>  0:13
  - State "DONE"       from "STARTED"    [2014-01-28 Tue 20:17]
  :END:
  :PROPERTIES:
  :LAST_REPEAT: [2014-02-23 Sun 08:39]
  :END:
--8<---------------cut here---------------end--------------->8---

3. Mark the item DONE. 

Voilà... note the empty property drawer, the duplicate logbook drawers,
and the misplaced :LAST_REPEAT:

--8<---------------cut here---------------start------------->8---
* TODO Repeating task
  SCHEDULED: <2014-03-17 Mon .+2w>
  :LOGBOOK:
  - State "DONE"       from "TODO"       [2014-03-03 Mon 22:11]
  :END:
  :LAST_REPEAT: [2014-03-03 Mon 22:11]  :LOGBOOK:
  - State "DONE"       from "NOW"        [2014-02-23 Sun 08:39]
  CLOCK: [2014-02-23 Sun 08:26]--[2014-02-23 Sun 08:39] =>  0:13
  - State "DONE"       from "STARTED"    [2014-01-28 Tue 20:17]
  :END:
  :PROPERTIES:

  :END:
--8<---------------cut here---------------end--------------->8---

I am using...

 - Emacs version: 24.3.1
 - Org-mode version: 8.2.5h

...on Arch Linux.

Running edebug suggested that org-entry-put (which is invoked by
org-auto-repeat-maybe) places the :LAST_REPEAT: in the wrong place.
However, I couldn't discern why, since invocations of org-entry-put
otherwise seem to work fine.

Thanks,
Matt