Sorry I cant help you with possible service places in Mumbai... I did tour India with a DL650 last year, and it certainly did not seem like there would be many places, where you could get much model-specific work done for any big bike, unless it´s an Enfield. But if there are any such places, Mumbai or Delhi would be the two best bets, where to try finding them... still forget about them having any diagnosis systems for FI!
But what I can try to do for you, if you want, is ask a couple of Suzuki-workshops over here, who I think are pretty good in what they do, about the problem with cutting off. In order to do that, I would need an exact description of the problem, and the details of your bike as well.
One tip for Mumbai: it may cost a bit, but do book your accommodation well in advance, or in any case, don´t just pop up at 5 p.m., cos you may have serious trouble finding any place to stay, at any price. We went around Thane and the area near the airports, being stuck in the insane traffic jams for hours, before we could literally find one room available, and it was criminally overpriced, too. That was around the beginning of December (-07) so I dont know, maybe we were there at worst possible time.