Why was no Nobel Prize for Literature awarded in 1935?

As it is so often the case, an official reason given might not be the real reason for why something happened. In the case of the Nobel committee of that era, it is indeed the quasi official word that not a single suitable candidate was considered fit to receive the prize.

Another inquiring mind has asked this question before and claims to have had this answer from the committee itself:

to my question, for what reason was no prize awarded in 1935 I got this answer:

"the organization's guidelines state: if no work is found that is considered due to its importance and the guidelines given by alfred nobel, the prize money will be saved for one year. if no prize winner can be determined retrospectively in the following year, then the money will flow into a fund. In addition, there was more information about this in the guidelines:
http://nobelprize.org/nobelfoundation/statutes.html
_{Translated from: Der Literaturnobelpreis 1935 ...(User: Sakisan, 2007-05-08::12:52:37)/sub>}

From the viewpoint of a lover of literature or just a literary critic, this is of course quite absurd; or even absolutely absurd. But when looking at the previous choices for the prize things might become a little bit clearer. In the words of a critic of the whole process, the perspective might change a bit:

As to the early prizes, the censure of bad choices and blatant omissions is often justified. Tolstoy, Ibsen and Henry James should have been rewarded instead of, for instance, Sully Prudhomme, Eucken and Heyse. The Academy which got this exacting commission was simply not fit for the task. It was deliberately formed as 'a bulwark' against the new radical literature in Sweden and much too conservative in outlook and taste to be an inter- international literary jury. It was not until the 1940s — with Anders Österling as secretary — that the Academy, considerably rejuvenated, had the competence to address the major writers of, in the first place, the Western World. On the whole, criticism of its postwar practice has also been much more appreciative. Objections in recent times have less often been levelled against literary quality, rather referred, mistakenly, to political intentions. Also blame for eurocentricity was common, in particular from Asiatic quarters, up to the choices of Soyinka and Mahfouz in the 1980s.

Personnel weaknesses and a political agenda against much of what is now widely considered great literature… what's not to like about that?
But this proneness to failure is also almost understandable, when looking at the gargantuan task and impractical schedule the committee set for itself:

The Committee's first task is to trim down 'the long list' nowadays of about 200 names to some 15, which are presented to the Academy in April. Towards the end of May, this 'half-long list' is condensed to a 'short list' of five names. The oeuvres of these finalists make up the Academy's summer readings. At its first reunion in the middle of September, the discussion immediately starts, to end in a decision about a month later. Naturally, the whole production of five writers would be too heavy a workload for a couple of months but most names of the previous short list return the current year, which makes the task more reasonable. It should be added that in recent times a first-year candidate will not be taken to a prize the same year. In the background looms one of the main failures, Pearl Buck, the Laureate of 1938. A first-year candidate, she was launched by a Committee minority as late as 19 September, to win the contest a short time afterwards, without due consideration.

As was mentioned above, criticism of omissions and bad choices was often justified as to the early period of the Prize. The Academy headed by Wirsen made only one choice to get general acclaim by posterity — Rudyard Kipling, and then for qualities other than those that have shown themselves to be lasting. The score of the 1910s and the 1920s was better: Gerhart Hauptmann, Tagore, France, Yeats, Shaw, and Mann have been found worthy in several appraisals. The results of the period 1930-1939 are poorer. Two choices have widely been regarded as splendid: Luigi Pirandello in 1934 and Eugene O'Neill in 1936. But the period offers several laureates justly judged as mediocre — and they conceal as many cases of neglect: Virginia Woolf ought to have been rewarded instead of Pearl Buck, and so on. The Academy of the inter-war years quite simply lacked the necessary tools to evaluate one of the most dynamic periods in Western literature. The post-war Academy has in a quite different manner fulfilled the expectations of serious criticism. The Österling Academy's investment in the pioneers has received due recognition in many favorable assessments. Names like Gide, Eliot, Faulkner, Hemingway, and Beckett have won general acclaim. Some names less known to an international audience, like Jimenez, Laxness, Quasimodo, and Andric, have attracted criticism as insignificant, but been classified by experts as discoveries.

(From: Kjell Espmark: "The Nobel Prize in Literature", in: Agneta Wallin Levinovitz & Nils Ringertz (Eds.): "The Nobel Prize: The First 100 Years", Imperial College Press: London, 2001, p 137–159.)

A Nobel Prize is not awarded like an Academy Award for works created in the previous twelve months. Even if that would have been one of the criteria for selecting a winner, every year more than enough candidates would have been eligible for delivering great works over the years. This highly criticised committee with its often very questionable decisions did not manage to nominate and deliver the prize in more than one year.
Taken together it might read almost as if the committee did either not find a suitable candidate to their liking or to the liking of others in the majority of the first 50 years. This track record seems to indicate that 1935 was just not that special of a 'year in literature' or such an outlier in the behaviour of that committee.

At the time, Henry Suzzallo's National Encyclopedia claimed that:

The Swedish Academy decided not to award the Nobel Prize in Literature this year, declaring that no single person in the field of literature merited the award in 1935.

Whether this was accurate, it would not have been terribly unusual. The Peace Prize was likewise not awarded in 1935; it was retroactively given to German dissident Carl von Ossietzky in 1936.

In fact the Nobel Foundation's statutes provide for a prize to be "reserved" for a year if no suitable candidate was available for that year's award. If no one deserving could be found even after a year, the prize money is returned to the Foundation's funds.

§ 5. A work may not be awarded a prize, unless it by experience or expert scrutiny has been found to be of such outstanding importance as is manifestly intended by the will.

If none of the works under consideration is found to be of the importance indicated in the first paragraph, the prize money shall be reserved until the following year. If, even then, the prize cannot be awarded, the amount shall be added to the Foundation's restricted funds.

_{Statutes of the Nobel Foundation}

The Guardian article cited in the OP actually lists seven years where a retroactive award happened for the Literature Prize: 1915, 1919, 1925, 1926, 1927, 1936 and 1949. For instance, William Faulkner was awarded his 1949 Nobel in 1950.

One possible reason for 1935's omission may be that the Nobel Committee had been considering Roger Martin du Gard, for his novel sequence Les Thibaults. However, he was writing a seventh volume at the time, and perhaps this caused the Committee to delay a decision. As it happens, l'Été 1914 was published in November 1936 - too late to be considered that year.

Du Gard went on to receive his Nobel in 1937.