Apel:

All evidence points to the fact that the rhythmic performance of chant was an early practice which was lost after c. 1000.  One of the most eloquent testimonies comes from Aribo. (Willi Apel, Gregorian Chant, p. 132)

Bailey:

Most scholars who are not partisan would conclude that there is some historical authority for both positions, that in the earliest centuries the chant was sung proportionally, but in the later Middle Ages this practice was abandoned in favour of the smooth, so-called oratorical rhythm of the “plainchant.” (Terence Bailey, Commemoratio brevis de tonis et psalmis modulandis: Introduction, Critical Edition, Translation, p. 17)

Blackley:

The practice of proportional rhythm disappeared gradually during the eleventh century.  As liturgical offices proliferated, monks and cathedral canons glossed over the reciting-note longs in the ever-present psalm melodies, speeding them till there could be little differentiation between long and divided notes; the introduction of lines or staves on which to write the musical signs, as well as the use of chant melodies in part-singing, further weakened the tradition.  The gradual decline of proportional practice is evident in manuscripts of the period; the c. 1030 Ecternach Sacramentary, for example, differentiates between two longs and two shorts ascending, yet has only one sign for two notes descending.  But I believe that, as the practice of proportionality waned, some of its elements surely remained in the tradition and were put to good use. (R. John Blackley, Rhythm in Western Sacred Music before the Mid-Twelfth Century and the Historical Importance of Proportional-Rhythm Chant, pp. 15–16)

Cardine:

Although the first copyists of Gregorian chant were very imperfect in diastematic matters (the precise notation of melodic intervals), they very carefully notated the expressive part, the “musicality” in the melody.  The oldest symbols thus have a double signification—melodic and expressive.

As time went on copyists tried to represent the melodic intervals more exactly.  In this they succeeded but the interpretive particularities and the finesse of the notation gradually disappeared as a result and before long they came to write all the notes in an identical way.  Because of this simplified uniformity, Gregorian chant appeared to be, and in fact became, a “cantus planus”, that is, a chant free of all expressive values.  The term “plainchant”, which so often designates Gregorian chant today, should be discarded because it is based on a false premise. (Doms Eugène Cardine, Godehard Joppich, and Rupert Fischer, O.S.B., Gregorian Semiology, tr. Fowells, p. 8)

Gajard:

The rhythmic tradition, undisputed in the Xth century, by degrees became more and more dimmed, and was almost lost by the end of the XIth.  This too is odd.  The date which marks the arrival of the staff (fixing melody accurately upon lines) also marks the disappearance of the rhythmic tradition.  It comes to this: the invention of the staff, an undoubted blessing in certain ways, was at the same time the starting point of a definite decline.  So far there is no known manuscript with staff-notation which affords any rhythmic signs.  As to the MSS in neumatic notation of the XIIth and XIIIth centuries, these retain a few rare traces of the ancient tradition, but nothing of moment can be based upon them. (Dom Joseph Gajard, O.S.B., The Rhythmic Tradition in the Manuscripts, p. 17)

*Hiley:

There can be no doubt that rhythmic differentiation was an essential element in the practice of those choirs for whom the St Gall, Laon and other sources were written.  The fact that the Laon source is widely separate geographically from the others suggests that this way of singing chant was quite widespread.  How long it persisted is unclear. (David Hiley, Western Plainchant: A Handbook, p. 379)

Murray (and Mocquereau):

[The tenth] was the century during which the primitive oral tradition, especially as regards the rhythm, was rapidly being lost and forgotten, and less and less attention was being paid to the older manuscripts and their rhythmic indications.  Even when new manuscripts were compiled in the old notations, the scribes often reveal a misunderstanding of the old rhythmic symbols which they appear to use as merely graphic conventions.  In the musical treatises of the period, too, there are many complaints of the rhythmic decay of the Chant.  A typical example is to be found in the Commentary on Guido’s Micrologus by Aribo, written about twenty years after Guido’s death.  ‘A tenor,’ he says, ‘is the length of a note which is in equal proportion if two notes are made equal to four and their length is in inverse proportion to their number [i.e., two long notes are equal to four short ones].  So it is that in the old antiphonaries we often find the letters c, t, and m, indicating respectively celeritas, tarditas and mediocritas.  In olden times great care was observed, not only by composers of the Chant but also by the singers themselves, to compose and sing proportionally.  But this idea has already been dead for a long time — even buried.’

That the ‘proportional singing’ of which Aribo speaks was a question of proportional note-values is clear from the context.  That it had ceased to be the practice is equally clear.  In any case the four-line staff notation made no provision for rhythmic indications, and, by making it possible to sing at sight, destroyed ail ideas of depending on, still less preserving, an oral tradition.  But, as Aribo indicates, the old rhythmic tradition was already dead.  One of the chief causes of its extinction was undoubtedly the widespread practice of organum, in which the Chant was sung in parallel fourths and fifths.  This practice was already at least a hundred years old, and the tenth-century documents, Musica Enchiriadis and Scholia Enchiriadis, both explain that its characteristic feature was its slow pace (morositas).  Elsewhere we read that this slow pace made it practically impossible to maintain the proper rhythmic proportions between the short and the long notes of the Chant, even though these were still being indicated in the notation: ‘We still write down points and strokes in order to distinguish between the long and the short notes, although music of this kind [organum] has to be so solemn and slow that it is hardly possible to maintain rhythmic proportions in it.’

With the disappearance of rhythmic proportions between long and short notes, the original rhythmic tradition perished.  Henceforth the Chant was performed in notes of equal length, so that by the time the staff notation was introduced there seemed to be no need to do more than write down the precise notes and intervals.  The state of affairs is thus described by Dom Mocquereau: ‘Originally in the oldest neumatic notations it was the rhythmic tradition that was perhaps better expressed than the melodic intervals. . . .  But this tradition did not maintain itself for long, and the Guidonian notation only hastened its decline.  Everywhere it did away with the letters and signs which, in the primitive notations, indicated the rhythm, and, from this point of view, far from being an advance, it was a retrograde step.’ (Dom Gregory Murray, O.S.B., Gregorian Chant according to the Manuscripts, pp. 7–8)

Rayburn:

As early as the eleventh century, however, a rhythmic disintegration had begun, and theoretical writers of the period noted this decline of proportionalism with dismay. (John Rayburn, Gregorian Chant: A History of the Controversy Concerning Its Rhythm, p. 5)

Vollaerts:

The combination of causes such as; [sic] lack of understanding and interest, lack of education in singers, lack of copyists familiar with the true tradition and with the meanings of signs and letters, failure of the memory by which for a long time the chants were mainly sung, together added to the use of part-singing, accelerated the crumbling and ultimate disappearance of the original rhythmic tradition. (Fr. Jan W. A. Vollaerts, S.J., Rhythmic Proportions in Early Medieval Ecclesiastical Chant, 2nd ed., p. 219)

Vos:

It is a fact that the fashion for organum [diaphonie] resulted, after a relatively short time, in universally and definitively distorting the primitive Gregorian music.  It then became a plainsong.  This fact emerges clearly from the comparison of the earlier books with the later Gregorian chant books. (Fr. Joseph Vos, “La notation neumatique et la tradition rythmique grégorienne” in Scriptorium, vol. 9, no. 2, p. 230)

Weaver:

Mocquereau, Cardine, and Vollaerts share the idea that there was a medieval rhythmic tradition that was already falling into decline at the time of the earliest notations. (Charles Weaver, André Mocquereau’s Theory of Rhythm, p. 99)

*See here for an alternative narrative from David Hiley, along with my commentary.