For recurring tasks (say a daily subscription status check) you might want to look into Celery Beat (
http://celery.readthedocs.org/en/latest/userguide/periodic-tasks.html). I runs on Celery (which is in the Open edX stack out of the box).
I haven't used it personally, so I can't vouch for it, perhaps someone else with more Celery experience can chime in. Otherwise you can brute force it my writing a django management command (typically in a /management/commands subdirectories in the Django "apps") and trigger through OS level timers/schedulers.
You will still have some additional work to do regarding a payment provider gateway. I'm only familiar with CyberSource, but recurring billing is probably offered through most payment gateways - but you'll still have to tie it into the eCommerce flows that are currently in lms/djangoapps/shoppingcart.
Please note that a team here at edX is working on a next generation eComm engine (our internal project is nicknamed Otto) based on Django Oscar, a standard Django library. I'm not aware of any plans by that team to do subscription model support for our own internal needs, but you should first decide if you might want to take on working with the existing shoppingcart platform or work towards the newer platform.
Sorry I can't give a concise answers, but I think quite a few of the pieces are in place.
Best,
Chris