My friend and colleague, Julia, who is currently completing her dissertation research in Jaipur, has generously written up her visa renewal experience. She describes a process significantly different than what I went through in Delhi, but it backs up my earlier assertion: nothing would ever get done without the help of AIIS in general, and Kumarji in specific.
My main advice for getting the visa renewed at your local FRO is to have all of the Indian administrators in your life on speed dial on your mobile phone, ready to talk with any bureaucrats you encounter. If we hadn't had the local AIIS office helping us, we would have been completely lost, and would have wasted an enormous amount of time to frittering, waiting in offices, and running back and forth gathering bits of paperwork. Having AIIS's assistance also helped avoid the awkward question of whether, and to whom, to offer some "additional under the table fees." I don't know if AIIS just has the system figured out, or if they're greasing the wheels somewhere, but those issues never came up.
First, about two months before our visas expired, we went to visit Kumar, the office administrator at the AIIS's offices in Jaipur, affiliated with their language program. Because AIIS deals with an enormous amount of volume in bureaucractic visa work in Jaipur, Kumar knows the ropes--he knows the peons who can get you the right guy to talk to and the FRO office people have his number. He told us that it was too early to apply, and that they wouldn't take our forms yet, saving us a trip to the FRO. Several weeks later, we arrived at the FRO in Jaipur, where they told us they couldn't renew my research visa. I told them they could, they told me they couldn't, and that I needed to go to Delhi. It was pretty clear that the main issue was a lack of experience with research visas, so I called the person in charge of junior scholars at the Fulbright offices in Delhi and handed the phone to the FRO guys. She convinced them that what we wanted was possible. Then I talked a bit about how I knew Kumar, and we had tea with the FRO guys, and after some last minute photocopying of forms we needed, they took our paperwork--and, disconcertingly, our passports. They were dreadfully vague about when we would see our passports again--"you know," they said, "the Indian government is so slow." I got the mobile number for one of the FRO guys and we went on our way.
At this point, our paperwork was sent to the Secretariat, the state government offices, for approval. Several days after dropping the forms (on Kumar's instructions), I called the guy at the FRO to confirm that the forms had been sent and to get our paperwork's "dispatch" number, so that we could find the forms at the Secretariat. About two weeks later, we went--WITH KUMAR--to the Secretariat, where he talked to the right guys to actually get our forms out of the paperwork piles and moving along; without this, he said, our paperwork never would have moved. Do NOT go to the Secretariat for the first time by yourself; it is really huge and overwhelming. Without Kumar we literally would not have been able to figure out how to get in the door. They told us to return a few days later for our completed forms and passports. We did. We actually SAW our passports move from desk to desk, getting signed and written on, but after a several hour wait, it turned out that "Sahib," whose signature was necessary, wasn't in, and we had to return the following day when, at last, we received our passports and other paperwork in a sealed brown envelope, which Kumar had instructed us not to open.
At this point, we brought the envelope across the city, back to the FRO, where they opened it, stamped up our visas and our "residence permits" and signed everything twice.
From dropping off our forms and passports to having our passports, with visas, in hand, took about 3 weeks, total. This included both an extension of my research visa and of my partner's dependent spousal entry visa. It's a little terrifying being without your passport for that amount of time; make color copies if you haven't already, and don't plan any travel for that period.