If you have the time and time for a 3rd time and you really really want to go to a top 15 school, I'd say go for it. I know a friend of a friend who took the GMAT 5 times. He's eventually got into several top 10 schools. And he's an int. student. So don't give up. And take the GMAT 2 or 3 times is very common. Almost everyone I know took it at least 2 times. So I wouldn't worry about it at this pt.
As far as your study goes, if you've been studying a lot but not seeing much progress, have you thought of trying a different study method? Were you studying by yourself, may be you could consider take a class? Get a partner? Which books were you using, I've found that some study guides are horrible and using them is actually detrimental to my score. There're plenty of suggestions floating here on this forum. If you are weak on math, do the gmatclub challenges
, if you are weak on verbal, read the MGs and the WSJ everyday.
Considering that you come from an Indian engineer background, I'd say that a low gmat score will put you at a greater disadv. than if you come from other bkgds. That's b/c many Indian candidates also come from engineering bkgd and many Indian candidates have very high GMAT scores. So adcoms will likely compare you w/other Indian engineering candidates.
You will really need to distinguish yourself from the rest of the pack in this case. If you have a high gpa from a top college, that'll help if your gmat isn't as high, esp. if you majored in a demanding subj. like engineering.
I think the social entreprenurship is a great angle, plus your rural background. You said you're the 1st eng. in family, are you also the first person, or first woman to enter college? Schools luv those first in family to attend college type of bkgds. Anything that shows you arises from humble bkgd, overcome hardships makes compelling essay topics. Anything that shows you are not just another Indian engineer will help your case.
Hope this helps. Best of luck!