Great, thanks for all the excellent advice and code!  I decided to approach
this locally with a capture template and put my repeating APPT tasks under
my Calendar headline.  I created this capture template that does the job:

(setq org-capture-templates
      '(("c" "Calendar" entry (file+headline "~/grantMain.org" "Calendar")
             "* APPT %?\n%i\n%a\n:PROPERTIES:\n:REPEAT_TO_STATE:
APPT\n:END:\n" :prepend t)))

Grant

On Fri, Nov 21, 2014 at 1:56 PM, Brady Trainor <algebrat@uw.edu> wrote:

> Grant Schissler <grant.schissler@gmail.com> writes:
>
> > Hi Org-mode Users,
> >
> > I am trying to change the behavior of marking a repeated task as DONE.  I
> > would like the task to return to the current TODO state rather than the
> first in
> > the TODO sequence or a fixed state.  For example,
> >
> > ** APPT Lunch with Mallorie
> > <2014-12-04 Thu 12:00 +1w>
> >
> > should return to APPT, not TODO or some other predefined state as in the
> > current behavior:
> >
> > TODO Lunch with Mallorie
> > - State "DONE"       from "APPT"       [2014-11-21 Fri 10:56]
> > <2014-12-11 Thu 12:00 +1w>
> >
> > I am sure that customizing the org-todo-repeat-to-state will do the
> trick, but
> > sadly, I have had the time to learn elisp well enough to perform this.
> >
> > Any help would be much appreciated.  Please let me know if you have
> > questions.
> >
> > Thanks for the support and to all those that make org-mode great!
> > Grant
>
> I haven't tried any of the following, and there may be better solutions,
> but...
>
> It looks like the variable you mention reads as (via C-h v
> org-todo-repeat-to-state RET and follow link to source),
>
> #+BEGIN_SRC emacs-lisp
> (defcustom org-todo-repeat-to-state nil
>   "The TODO state to which a repeater should return the repeating task.
> By default this is the first task in a TODO sequence, or the previous state
> in a TODO_TYP set.  But you can specify another task here.
> alternatively, set the :REPEAT_TO_STATE: property of the entry."
>   :group 'org-todo
>   :version "24.1"
>   :type '(choice (const :tag "Head of sequence" nil)
>                  (string :tag "Specific state")))
>
> #+END_SRC
>
> It looks like this variable will not allow to recall the previous TODO
> state. But you could make a separate TODO_TYP set.
>
> Depending on whether you define your TODO states in an init file or
> per-file base, you could try an extra line in your org file "header",
>
> #+BEGIN_SRC org
> ,#+TYP_TODO: APPT | DONE
> #+END_SRC
>
> or an extra block in your org-todo-keywords variable
>
> #+BEGIN_SRC emacs-lisp
> (setq org-todo-keywords '((type "APPT" "|" "DONE")))
> #+END_SRC
>
> Another solution according to the above would be to use a property drawer,
>
> #+BEGIN_SRC org
> ,** APPT Lunch with Mallorie
> <2014-12-04 Thu 12:00 +1w>
> :PROPERTIES:
> :REPEAT_TO_STATE: APPT
> :END:
> #+END_SRC
>
> You can get this via C-c C-x p repeat_to_state RET APPT RET.
>
> Interestingly, there is a function in the same source file,
> org-auto-repeat-maybe, which suggests that it does exactly what you ask for.
>
> #+BEGIN_EXAMPLE
> org-auto-repeat-maybe is a compiled Lisp function in `org.el'.
>
> (org-auto-repeat-maybe DONE-WORD)
>
> Check if the current headline contains a repeated deadline/schedule.
> If yes, set TODO state back to what it was and change the base date
> of repeating deadline/scheduled time stamps to new date.
> This function is run automatically after each state change to a DONE state.
>
> [back]
> #+END_EXAMPLE
>
> I can see in the definition of the function it has an expression
> org-last-state, so maybe that suggests there is a way built-in (or intended
> to?), but I only took that quick look at the source.
>
> --
> Brady
>