I had 5 or 6 interviews and the process took about 2 months (which is lightening speed for Ashoka)
The process is lengthy, opaque and awfully subjective on the part of the interviewer. Ashoka hires for entrepreneurship, which is as fuzzy as it sounds.
The organization is brimming with very smart, capable, talented people who are deeply committed to the organization and it's mission. For the social entrepreneurship/change space working at Ashoka is kind of like working at McKinsey. That said there are probably a few organizations that won't want to work with you if you've been there, but not many (and that's not been substantiated just my opinion).
If you want to work here, make sure you are burning with desire to do so.