I've had varied levels of success but the most consistently successful model has been a leverage model. By this I mean that there is one person in the agency whose primary (often sole) job is to manage the communication with the client. This person is representing the customer to the development team. The key skill that this person needs is that they are familiar with and can navigate the culture of the client as well as the culture of the development agency.
For Indian teams this usually has been someone Indian who has worked for a number of years in the US, the UK or Aus but it doesn't have to be. Note, I have generally worked for US or UK companies so YMMV.
Ideally, the go between is physically located with the client. This really helps in the US as the timezone headaches become an internal agency issue to deal with. If they're not co-located with the client then this can still work but the go between has to be really, really good.