I am a green card holder and received it on Oct 21, 2011. I moved to India on Nov 21, 2013 . I applied for a re-entry permit before I left USA and I have a permit valid up to Mar 10, 2016.
See clip from Attorney Rajiv S. Khanna's conference call video that addresses this question.
I want to point something to you, there is lot of misconception about re-entry permit. Reentry permit does not give you an irrevocable right to stay away from USA, but it is as close as you are getting security in maintaining your Green Card. Reentry permit simply says this; the fact that you are away for two years cannot be used by itself as a ground for revoking your Green Card. If on the other hand, it appears that you have no intention of coming back and you are abandoned your intention to live in the United States, they will take away your Green Card even if you have the Reentry Permit.
As a practical matter, USCIS does not look behind the Reentry Permit. So far I have not seen any cases. But don't think it's a foregone conclusion just because you have Reentry Permit, you are hundred percent protected. No such thing.
Another thing to remember is you don't have to visit USA even once, while the Reentry Permit is in play. But you must enter USA before the Reentry Permit expiration, if you want to extend it. And extension can only be done while you are physically present in the United States. You cannot send application via courier from India to USCIS, like as you asked. That's the way it should be.