John Lyly's Euphues novels are among the first novels in English. But they were also among the most faddish. While exceedingly popular for several years, in the late 1570s and early 1580s, their reputation and popularity did not outlast the early Elizabethan court. Their overwrought, precisely structured, mannered rhetorical style would be parodied more than it was imitated, subsequent to the 1580s. Lyly is more appreciated today for his plays, where his excesses are not quite so manifest, nor so out of place (as they are in long form prose narrative).
I would contend that this is necessarily the earliest in English history that we may observe such a case (of a literary fad wherein the literate class embraces, then casts off, a work or series). Before the Elizabethan era, we simply don't have an active and well-attested literary critical sphere which can develop opinions and preferences among the literati, and record those opinions for posterity.
The simplest answer is yes, some texts have become crazy popular at points in history and then suddenly fall out of favor, usually because of a perceived issue with the author or the text itself.
I think an important thing to keep in mind first off is that a lot of books and authors fall in and out of favor over time, especially within the literary canon. I think a lot of people think of the canon as this rigid but mysterious "set" of the "Whacking good classics" like Dickens, Shakespeare, Milton etc. This isn't really the case, as many of these authors go through periods where one or more of their books are less popular than others, or one book will be radically more popular over time. and while the three I just named have been more-or-less popular since their lifetimes (I'm less sure on Milton, but I know Paradise Lost sold like hotcakes) many other of the canonized writers haven't always been famous, such as Melville. So it is a bit odd when you look back to see who was and was not popular at their time, and at various times in history. I think most famous authors of today have undergone waning bouts of popularity, and certainly most if not all famous texts have gone through periods of obscurity.
Take for example, D.H. Lawrence. He was gaining popularity in England at the start of his career, though never really critically adored. Then opinion turned viciously against him, when Lawrence began his affair with Frieda von Richthofen, a married German noblewoman, and as anti-german sentiment began to rise, Lawrence and Frieda became more and more maligned, eventually culminating in his voluntary exile in 1919 from England. Until his death in 1930, he was generally reviled and heavily censored, and his works were relatively limited in renown until the Obscenity trial over Lady Chatterly's Lover in the 1960s, where he became a much more widely read and accepted into the canon of English Modernism. To further controversy, Lawrence was accused of being sexist/anti-feminist in his writing, and has the stink of Facism on him, so he is occasionally maligned or removed from survey courses because of this. In addition, as Lawrence does not "fit" into the Bloomsbury-centric vision of British Modernism nor really the Edwardian sense of early 20th century British Fiction, he can be sort of hard to place, further leading to his exclusion. Lawrence's works seem to be having a bit of a revival recently, though that might just be my Modernist colleagues talking.
On the completely different side of the spectrum, there's the shifting popularities of Medieval texts over the years. The Canterbury Tales have always been pretty well received, but certain tales have enjoyed more or less favour over the years. During the Middle Ages, the most common tale was the Clerk's Tale (we assume this because it is the manuscript that has the most surviving copies), which is Chaucer's retelling of Bocaccio's Griselda tale with slightly different focuses. This tale is much less popular today, especially when compared to something like the Knight's Tale or The Wife of Bath's Tale, which are more commonly anthologised or read today. This probably has a lot to do with how problematic the Clerk's Tale can seem on first read, as Griselda basically is mistreated and abused by her husband for 1000 lines, only for it to end in their happy marriage and reunion of their family, and an odd Envoy (either a narratival interjection by Chaucer or an epilogue by the Clerk) that is a warning to women to not be Griselda and speak up, which seems to go against the message of humility. The Griselda story was remarkably popular, often sans Envoy, with many probably because it fell into the same sort of tradition of the various vitas that were popular in the 14th and 15th century that centred on women and subjugation/abjection in the face of the Lord (or in Griselda's case, her lord) and is also a "translation" of a well known story by Boccaccio. As part of the Canterbury Tales, the Clerk's Tale has pretty much always been included, but it's not really a favourite any more, due to the above problems. So one could say it had its moment in the 14th/15th century, but has since kind of fell to the sidelines, relative to the other tales.
I think long story short, Literary fame is fickle in the long arm of literary history, so lots of texts become very famous and then quickly fall off. I think this process may be a bit faster nowadays, with the rise in a literate media-consuming audience, but a lot of our foundational texts have gone through periods of obscurity or neglect.
Lawrence Sources:
D.H. Lawrence Review. Literature Resource Center 1969 - current (seems last one came out in 2013, vol 37, could just be my uni's access though) - I'm not a Lawrence scholar by any means, but I think the establishment of a peer-reviewed journal dedicated to the author seems to be a good indication of their mark in the canon. I'd review the journals a bit to give more indication in the changing moors of criticism, but the digital copies only go back to 2010.
Millett, Kate, 1969 (2000). "III: The Literary Reflection". Sexual Politics. University of Chicago Press. ISBN 0-252-06889-0. - Not a Fan of Lawrence
Deleuze, Guattari, Gilles, Félix (2004). Anti-Oedipus: Capitalism and Schizophrenia. London: Continuum. - Bit more sympathetic fan of Lawrence.
http://www.dh-lawrence.org.uk/ - Apparently the University of Nottingham runs a page on him. Pretty basic, but it's a good primer.
Chaucer Sources:
Farrell, Thomas J. "The "Envoy De Chaucer" and the "Clerk's Tale"" The Chaucer Review 24.4 (1990): 329-36
Chaucer, Geoffrey, and Larry D. Benson. The Riverside Chaucer. Boston, Mass: Houghton Mifflin Co, 1987. Print.
http://sites.fas.harvard.edu/~chaucer/ - Good Basic Chaucer site ran by Harvard.
I should have more on Chaucer, though I might need to dig through my Zotero folders/bookshelves. First actual comment in the sub (have lurked for years) so I'm kind of nervous >_>
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