This answer has been percolating in my head for a couple of months now. Given that there haven't been any other attempts to answer it, I've posted it but realise its limitations in providing a clear answer to your question. It also does not speak at all to the question of Jansenism.
This is a great question but one that, unfortunately, has no simple (or short!) answer. Frustratingly, little appears to be written specifically about Latin in science but perhaps we can extrapolate from what is written about Latin in other areas.
The twin problems of declining use and declining literacy are a chicken-or-egg question. However, my reading on the topic (see references below) suggests that, initially at least, Latin fell out of favour not so much because of a decrease in Latin literacy but rather because of an explicit desire to replace Latin with the vernacular. That said, there is a pronounced geographical variance in the rate of the decline of Latin which can’t always be neatly explained. This would indeed seem to be linked to a rise in political power and nationalism but there are also issues of expression and fluidity at stake as well. Even so, science was the last bastion for Latin, resisting widespread use of vernacular until quite late. Gauss, as an example, continued publishing in Latin into the 19th century. Other areas of activity, writing and thought, however, had already abandoned Latin.
Latin had already started to lose ground in other spheres quite early for purely pragmatic reasons; vernacular language was simply more accessible and egalitarian. By the 13th century, for instance, Latin was no longer being used in commerce anywhere. Later in western Europe, Latin was no longer being used in government (e.g. the Ordinance of Villiers-Cotterêts in 1539 in France gave up all Latin in government), the law (e.g. the Statute of Pleading in 1362 in England ordained that court proceedings should be in English), or local administration.
However, this wasn’t happening everywhere in Europe. Eastern Europe, as an example, retained Latin as the language of officialdom for much longer. Hungary, for instance, encompassed speakers of Hungarian, German, Czech, Romanian and Croatian. Thus, Latin was useful as a neutral lingua franca. It wasn’t until 1790 that it was replaced with German. Latin in this situation then was a practicality.
Similarly, Dutch philosophers such as Spinoza or Huygens continued to publish in Latin simply because few people outside of the Netherlands spoke Dutch. Scandinavian scholars too published in Latin up until the late 19th century for the same reason.
This geographical variance is instructive. Latin’s decline was fastest in centres of political and cultural innovation; slowest on the peripheries. This suggests that Latin became outmoded or at least unsuitable for a new cultural climate. It also supports the thesis that Latin literacy itself didn’t decline (well, not at first). If it had, why would smaller, less influential countries continue to publish in it?
The French, in particular, sought to elevate the status of French above that of Latin, Greek and other vernaculars. This can be linked to a rise in French patriotism from the 1650s which itself is linked to growing political power. This is when we start to see French replacing Latin as a language of diplomacy. But more than a political or patriotic choice, the use of vernacular could be used as a statement of principles.
Consider the example of Descartes who published Discours de la méthode in French in 1637. This was subsequently translated into Latin but not until 1656. This was a deliberate choice due to Descartes’ desire to distance himself from the scholastics and to be understood by “even children and women”. The link between one’s political stance and language is even more obvious in Hobbes. His De Cive of 1650 was originally published in Latin but quickly translated into English. Leviathan (1651), however, was published in English and only translated into Latin in 1658. This is because Hobbes was explicitly writing for an English post-Civil War audience. His message: that all legitimate political power must be "representative" and based on the consent of the people. This surely is a message to be given in the people’s own language.
For similar reasons of accessibility, Luther (in 1522) and Tynedale (in 1525) had already translated the Bible into German and English respectively. Speaking of his translation, Luther said “we are removing impediments and difficulties so that other people may read it without hindrance."
Furthermore, Latin increasingly came to be thought of as a language of the past and of imitation.
Natural, spontaneous, nuanced expression in Latin was difficult. Even as early as the 17th century, Latin was seen as an ossified means of expression and subsequently fell out of favour for new, creative literary output. The last era of creative literary output in Latin in England, for example, was ca. 1530-1640, with vernacular literature replacing it. In fact, in England, Latin never really had a strong hold on the market. As early as the late 1500s, Latin works only accounted for 10% of publications. In France, by 1764 Latin titles accounted for less than 5% of publications. And in Germany, by 1681, German books outnumbered Latin ones.
In France, defenders of Latin were seen as snobbish, unpatriotic, uncreative, cowardly and hidebound. The following verse by Desmarets written in 1675 illustrates this (quoted in Argaud):
Amans trop obstinez de la langue Latine, Qui toujours attachez sur les mesmes écrits, Ne s’éloignent jamais de leur vielle routine ;
Qui n’aspirant qu’au rang d’imitateurs, Ne peuvent s’élever plus haut
que leurs Autheurs. Pauvres imitateurs, ne faites point les braves …
Lovers who persist too much with the Latin language, Who always stick to the same writings, Are never far from their old routine;
Who, aspiring only to the rank of imitators, Can’t elevate themselves
any higher than their Authors. Poor imitators, don’t pretend to be
brave … (caveat: my own translation!)
These same constraints must have also been felt in the sciences. Why it held on for so long, I can only speculate. Tradition may be one reason, prestige and perhaps even credibility another. Apparently, Gauss published in Latin “not from internationalist sentiments but at the demands of his publishers” quoted here. Perhaps too there was an idea that universal ideas should be able to be expressed in a universal language. For Pike, writing in 1918, Latin was abandoned as an international scientific language because it was simply:
felt to be a restraint upon untrammeled expression of thought. The
classicists did all they could to assist its disuse by insisting upon
the employment of a Ciceronian diction which science had outgrown.
Nothing is so restive under restraint as the expression of creative
thought … Modern thought expresses itself naturally in languages of an
analytic, not in those of a synthetic, character. It takes long and
severe training to accustom the modern man to express himself readily
through the synthetic medium of Latin. (p. 53)
Thus, perhaps Latin became less and less a useful medium for expressing increasingly complex ideas. It did, however, retain its hold in the “descriptive sciences” – astronomy, geology, palaeontology, medicine, zoology, botany – precisely because of its strict precision which is tailor-made for taxonomic labels.
Evelyne Argaud, ‘Les enjeux des représentations des langues savantes et vulgaires en France et en Europe aux XVIe et XVIIe siècles. Affirmer des prééminences et construire une hiérarchisation’, Documents pour l’histoire du français langue étrangère ou seconde, vol. 23, 2009 (mise en ligne 2011).
Nicholas Ostler, Ad Infinitum: A Biography of Latin, Harper Collins, London, 2007.
Joseph B. Pike, ‘Can Latin be Revived as an International Scientific Language?’, in The Classical Journal, vol. 14, no. 1, October 1918, pp. 48-55.