Who remembers bands like Stallion or Scheme now?

Hardly anyone, and for perfectly explicable reasons. In the Glasgow of the early 1980s the balance of musical power shifted fatefully, from long-haired highway rockers to a new breed, the so-called Sound of Young Scotland. Symbolically, the crown passed; from Alex Harvey to Edwyn Collins. And the coronation took place in the Rock Garden, a bar on Queen Street. One Paul Joseph Moore was a barman there and fell one night into conversation with a customer, another of the floppy fringed hopefuls who filled the place, debating how far up the chest a bass guitar could decently be worn. "I'm in a band," he told Moore, then paused. "As you probably know -"

Moore also was in a band and his colleagues, Robert Bell and Paul Buchanan, found the comment just as preposterous. Among the three the comment became a kind of nightmarish catchphrase. These three earnest boys from Bishopbriggs found the suggestion risible, that playing in a band was in any way glamorous or glorious, a cause for vanity or congratulation. They aimed to become the antithesis; a band as modest, and as covert, as possible.

In this mission, the members of what became The Blue Nile have proven signally proficient. Few modern musicians have so doggedly kept their heads so far below the parapet. Famously, The Blue Nile do virtually nothing, very slowly. Over the life span of the band, they have recorded an average of just one song a year. The gap between their third album and their fourth was longer than the recording career of The Beatles. They may have disbanded in 2004, though nobody's certain, least of all Paul Buchanan, the band's songwriter, vocalist and focus. Either way, The Blue Nile remains what it ever was: a riddle, wrapped in an enigma, wrapped in a raincoat – the source of music adored for its transcendent world-weariness.

Theirs has been a career of two halves, however. The early, glory years are celebrated in a brace of reissues available on November 19. A Walk Across The Rooftops, the 1984 debut, was a record of spare synthetic majesty, a Hillhead hybrid of Brian Eno and disco, of Frank Sinatra and Kraftwerk; or, as the critic Caitlin Moran wrote, "the sound of cities cooling down, of pavements shrinking, and streets becoming quiet". Its successor was Hats in 1989, on which the melancholy assumed symphonic proportions.

And then it all began to crumble. If the band's founding principle had been the avoidance of cliche, they honoured it with a modus operandi of suicidal ingenuity. For instance, they refused to appoint a manager. Members sited themselves on disparate continents. They recoiled from live performance, on grounds that grew increasingly spurious; particularly their requirement for an "impractical" number of synthesisers. A million-dollar deal with Warner was signed, seemingly without Bell and Moore being aware of the fact.

Ed Bicknell was the manager who took Dire Straits to global renown, and he was there to administer The Blue Nile the last rites. "Even by the standards of our profession," he told me, "I'd never heard a more convoluted and, to say it bluntly, f***ed-up situation." Yet two further albums emerged: in 1996 Peace At Last, a collection of breezy Americana and, in 2004, High, a muted parp of wine-bar soul. Somehow, the austere European stylings of the early work had undergone a boil wash and become something else completely. In the end, Paul Buchanan surveyed the psychic wreckage of an approach that had been tentative, neurotic and baffling. "Everything goes away," he told me "Your relationships go, everything goes. It all goes. And coming down is hell." Today, Moore and Bell live quietly in the West End of Glasgow, with partners in the higher echelons of broadcasting; Buchanan is sporadically a solo artist and haunts Byres Road as ravens haunt the Tower of London. It is one of the saddest, most profligate stories in British music history.

But what persists is the legend, the sense that The Blue Nile captured something rare and exquisitely mournful, something ineffable. A Walk Across The Rooftops and Hats have carried the legend unto the next generation, one kept hungry by the ongoing Blue Nile drought. Which is what makes so intriguing the idea that the albums are receiving finally the deluxe, double-disc, previously unavailable, with-added-Korean-B-side treatment. The band may have shut up shop, but surely the archives will yield some crumbs of sustenance?

Of course they won't. That would be too predictable. Again, standard band practice has been side-stepped. As deluxe reissues go, these sets leave so much to be desired and, like the career in toto, are passive-aggressive to a fault. Both albums have been remastered and, admittedly, they are worth hearing. This might sound counter-intuitive given that A Walk Across The Rooftops was recorded to be a demonstration disc for a manufacturer of audiophile turntables and Hats, similarly, was given all the sonic grooming the era could afford.

But back then neither album was released on compact disc, at the insistence of Linn Records, the band's equally pernickety sponsor. They were mastered for vinyl and, after unsympathetic transfers, have sounded thin ever since, particularly Hats. The remasters restore to both some punch and presence: to the metallic funk and Bartok strings of Tinseltown In The Rain; or the swooning Glasgow noir score of The Downtown Lights.

But, oh, where to begin with the bonus discs? It needs to be conceded that The Blue Nile have form in short-changing fans. As early as their first major single, Stay, they took exception to the convention of the B-side, preferring to offer an album track, Automobile Noise, with its vocal removed. This strategy was revisited throughout their career (and on Buchanan's recent solo album Mid Air). The upside of this was that the band were spared the trouble of cleaning the ashtrays and leaving the house. The downside was that, three decades later, there would be nothing to put on bonus discs.

Hence the laughably shoddy nature of these offerings; assembled, the press release is happy to admit, by Bell and Buchanan themselves. On A Walk Across The Rooftops we find I Love This Life and The Second Act, both sides of the band's debut single, both appearing on a Blue Nile release for the third time. There are Rave Dad remixes of three songs from the Rooftops album: Heatwave, Tinseltown In The Rain and Stay; basically the original recordings garnished with whichever drum loop or bit of tisky-tisk percussive parsley could be downloaded free. There is Regret, B-side of Tinseltown In The Rain, and also St Catherine's Day, the sole "new" track, a strong piece well-known from bootlegs, though here it sounds as if a contemporary re-recording is used; which, you must admit, is a monstrous cheat.

A similar trick is played with Christmas, the only new song on the Hats reissue, a sleepy lump of musical cotton wool, augmented here with a hilarious whispered "Wake up!" that brings to mind David Brent's version of If You Don't Know Me By Now. Beyond that there are two live tracks, Seven AM and Headlights On The Parade, offering nothing new beyond a few scraps of wristy funk guitar; and early takes of Let's Go Out Tonight and Saturday Night, distinguishable from the originals only by a man in a lab coat. The Wires Are Down is decent, much as it was when first released in 1989.

The remastered original albums aside, the package has an improvised feel, like someone assembling a kids' Christmas stocking from a newspaper and a Winalot box. Yet there's no shortage of decent material in the vaults: the version of Easter Parade recorded with Rickie Lee Jones, B-sides like Our Lives and Halfway To Paradise; off-cuts such as Young Club and Broadway In The Snow; glorious live shows from Glasgow, London, New York; even Flags And Fences, the obscure US tour documentary from 1992.

In the end, it needs to be asked: why did The Blue Nile so keenly pluck defeat from the jaws of victory? Temperament, in my opinion. They were just too educated, too well-raised, too diffident to prosper in the multi-coloured snake pit of 1980s British pop. And too anal. The answer lies most probably in the realms of psychology; for some reason these three cautious and highly strung young men were uneasy with, or ill-suited to, the profound abilities revealed here. "It's not enough to have talent. You have to have talent to handle the talent," said Sir Peter Hall. As you probably know.

Allan Brown is the author of Nileism: The Strange Course Of The Blue Nile (Polygon, £8.99). The two-disc remastered collectors' editions of A Walk Across The Rooftops and Hats are released on November 19. A "Communal and Audiophile Listening Experience" of A Walk Across The Rooftops, organised by Classic Album Sundays, will be held at The Berkeley Suite, Glasgow, on November 25, tickets £6 (loudandclear.eventbrite.com)