BlackBerry has long enjoyed a devout following in India. However, its fan base has become decidedly niche in recent years as Androids have swamped the marketplace, reducing this iconic Canadian phone maker's numbers into insignificance — below 1 percent, at last count.

So it should come as no surprise that Amazon India has revealed that it just can't keep up with the demand for the new, unusual-looking 4.5-inch square Passport, which fields an aspect ratio of one to one, launched here on October 11.

Not only has the company exhausted initial stocks, it also said that the Passport has elicited a massive amount of interest from the Indian public — much of it from smaller cities and towns that are not in the top eight metros of the country.

"Amazon.in has received orders for the BlackBerry Passport from 115-plus cities across India," declared a recent statement from the company.

Normally, China would offer BlackBerry chief executive John Chen a large market to lean on, but there are security concerns about BlackBerry's proprietary messaging service, so this means that India looms large as a market he absolutely needs to win in. Thus far, it's been a miserable outing, with market share falling precipitously from 14.8 percent in the April to June quarter in 2010-11 to 7 percent in 2012, 2.9 percent in the first quarter of 2013, and finally to a bleak all-time low of 0.5 percent in the first quarter of 2014, according to IDC.

The Passport has given the company new life in India, just as it did in North America a month ago, when it sold out in six hours on the company's website and 10 hours on Amazon, according to Chen.

In India, prior to the Passport's success, BlackBerry also made significant strides in its services play — close to 50 percent of its consolidated revenue stream — by launching a wired healthcare service, thanks to an investment in NantHealth, a US-based healthcare technology firm.

Patients, especially those in remote areas, can soon be monitored by a large urban hospital, using a secure, cloud-based network that also allows for delivery and payment systems, along with critical decision making that rides on data and analytics.

Of course, not everything seems rosy for the phone maker globally; Todd Coupland of CIBC markets has revised his forecast of BlackBerry phone sales.

"Shipments, however, are being held back by supply constraints for unique screens and keyboards that will limit any upside in fiscal Q3," said Coupland.

Meanwhile, the phone is being sold for as much as $1,825 in the gray market, which is double to triple what it normally costs. And word on the street is that Indians are willing to go to extreme lengths to get their hands on one.

Someone who isn't too concerned about the shortage of Passports is Chen. "I'm glad to have inventory issues. It shows that people want the phone," Chen said, speaking at an enterprise forum in Hong Kong. "We took a very conservative approach and didn't order too many."

Now, he will have to show that the company can satiate the raging appetite for his new phone before that hunger turns into frustration, much like it did with Xiaomi in India .