MUMBAI, India  When it was introduced in early 2009, the egg-shaped Tata Nano was billed as a modern-day people’s car, an ultracheap vehicle that would bring greater mobility to the masses of India and, eventually, the world. But those ambitions have stalled  for now, at least.

Though car sales have shot up across India, because of an economy that is growing at nearly 9 percent annually, sales of the Nano have been falling for the last four months. Its maker, Tata Motors, sold only 509 Nanos to its dealers in November  a stark contrast to the 9,000 it delivered in July. Last year, when media coverage and auto writers’ praise were stoking demand, Tata had orders for more than 200,000 Nanos, which has a list price starting at about $2,900.

But as Tata has struggled with problems like production delays and fires in some of the cars, rival cars like the Maruti Suzuki Alto have overtaken the Nano. The Alto, which starts at $6,200 here, had sales of more than 30,000 in November, making it India’s best-selling car last month.

On Thursday the Tata company announced that it would extend the warranty on the Nano, including those that have already been sold, to four years, from 18 months.