The abrupt resignation this week of William Lynch, the 43-year-old Barnes & Noble chief executive, was only the latest in a catalogue of troubles at one of the US’s biggest book chains. If this were a business whodunit, nobody could fail to spot the culprit: Amazon.

Still, with bookshops everywhere in retreat as the internet takes an ever greater slice of their trade, it seemed to many that a chain with its own dedicated e-reader — the Nook — could have the answer. But with Barnes & Noble’s device struggling to make any headway against Amazon’s Kindle, that strategy, and the US bookseller’s very survival, are now in question.

The business is already looking troubled. In the three months to 30 April, it saw revenues at stores open for at least a year fall 8.8 per cent, while total online and physical sales fell 10 per cent as some stores closed. In all, it made an underlying $118 million loss in the quarter — weighed down by a $177 million loss in the Nook division, compared with a $77 million loss a year earlier.

The Kindle has swept all before it in the global e-reader market, and Amazon has millions of stores right on peoples’ desks, smartphones, and tablets through its website and Kindle app. Authoritative estimates for the UK market underline the Kindle’s power, with Amazon believed to account for nine out of 10 e-book sales — an indication of the Kindle’s penetration.

Lynch, a former executive at smartphone company Palm, was hired from Home Shopping Network (HSN) in February 2009 to head Barnes & Noble’s online business, where he expanded its digital offerings and oversaw the Nook’s launch. In February 2010 he was made chief executive, bringing his e-commerce skills to bear in charge of a chain with 675 bookstores in 50 US states, and 686 college bookshops. Now, he’s gone.

But this business whodunit has a twist: the question being asked now is whether the e-reader category, including the Kindle, introduced in November 2007, has a long-term future. Global sales are plummeting in the face of competition from tablets — like the iPad — and smartphones.

“[Worldwide] e—reader sales have dropped dramatically to 17.9 million in 2012, and will reach only 16.1 million in 2013,” says Hughes De La Vergne, who follows the sector for the research group Gartner. “Tablets costing $199 or less have become much more common, and make it difficult for many users to accept the need for a stand-alone e-reader.”

According to eMarketer, another analysis company, the e-reader market is becoming saturated, if we take the dominant US market as an example. The number of US users has reached 63.5 million but people now buy tablets like the iPad mini, Amazon Kindle Fire HD, and Google Nexus 7 in huge numbers. The amount of US tablet users is expected to rise 31 per cent this year to hit 123 million.

With tablets outnumbering dedicated e-readers, the e-book business is expected to split in the tablet’s favour. On one side are the “bookworms” who buy a book a week or more, and want a dedicated e-reader; and then there is the much larger group who buy the occasional e-book, but prefer a tablet for its ability to deal with email, web browsing, and more.

Nook Media, the Barnes & Noble subsidiary that makes the Nook tablet, is already cutting back in the face of these changes. It won’t make any more of its colour touchscreen tablets, where it was the first to the market in November 2009, a couple of months ahead of the first iPad.

It has also slashed the price of the cheapest Nook reader to £ 29 in the UK. “That’s made it really take off at retailers,” says Lisa Campbell, senior reporter at The Bookseller magazine. “Some say they’ve sold out. But it’s famously tough here for companies that aren’t Amazon.”

While Amazon has never given Kindle sales figures, publishers are acutely aware that it dominates the e-book market, giving it the power to set book prices — even at a loss. Apple tried to break that stranglehold but this week a US federal judge ruled that the technology giant violated US anti-trust law by orchestrating a conspiracy to raise e-book prices with five big publishers.

“Apple did not conspire to fix e-book pricing, and we will continue to fight against these false accusations,” said Apple spokesman Tom Neumayr.

The publishers have already struck settlement deals worth tens of millions of dollars to be paid out to consumers who had been over-charged as a result of the conspiracy.

For those who are trying to make money from e-books, the reality is that Amazon is now the only game in town, says Andrew Rhomberg, co-founder and chief executive of e-book seller Jellybooks.com, which aims to be as easy to browse as a real bookshop.

“Amazon is the 800 pound gorilla,” Mr. Rhomberg says. “You can’t compete with them using the same model as they do. The booksellers’ idea of competition is to have Google or Apple knock the stuffing out of them. But the whole e-reader category is shrinking.”

In fact, says Mr. Rhomberg, the suspicion is that Apple, rather than Amazon, has grabbed all the Nook business after improving its iBooks offering and introducing its eight-inch iPad mini tablet last October. “But people still use their iPad and buy from Amazon, using the Kindle app,” he says. “It’s the logical place to go. Tablets need video and games and music, which Amazon does too. You can’t sell a tablet just with books.” But you can sell e-readers to those who love books. E-books are booming for genres such as thrillers, romances and crime, with bookworms in those categories downloading and consuming so regularly that 50 per cent or more of sales can be electronic. Coffee-table books which rely on pictures, meanwhile, don’t sell in any number on tablets. “We still haven’t mastered the layout and perception problems on tablets,” Mr. Rhomberg says.

For the Nook, there could still be a happy ending however, courtesy of a white knight. In April 2012, Microsoft spent $300 million to buy a 17.6 per cent slice of the Nook Media business; in effect valuing the tablet arm at $1.7 billion, more than its parent Barnes & Noble. Pearson, the educational publisher which also owns the Financial Times, took a 5 per cent stake in December for $89.5 million, nudging the value slightly higher at $1.79 billion. If Microsoft sees value in keeping the Nook going, it could get it at a fire-sale price.

Douglas McCabe, who follows the e-reader sector for Enders Analysis, says, “People are moving to using tablets; it may be that the window of opportunity around [e-reader] products was very short.” But he thinks the Kindle is the exception. “Because of the sheer scale that Amazon has built up over the years.”

According to Mr. McCabe, Barnes & Noble is under a lot of pressure. “It’s in trouble.” The only gleam of light, he suggests, is that the bookworms will continue to visit real bookshops. Barnes & Noble’s best chance might be to dump the e-reader and focus again on human readers.

“What they keep forgetting,” says Jellybooks’ Rhomberg, “is that Google didn’t defeat Microsoft by building a better operating system for the PC; it built a search engine for the internet. And Facebook didn’t beat Google by building a search engine. You just have to have a strategy that keeps you out of Amazon’s shadow.”