You can achieve this as late as the 19th century. This was a time of linguistic reform and standardisation. This mostly applied to spelling, but the case system was still taught in schools and accounted for. The spelling proposed by De Vries & Te Winkel in the second half of the 19th century still accounted for all elements of grammatical cases in words. This had changed by 1937, when the spelling proposed by Marchant went so far as to remove such elements. Famously, something like "op den stoel" became "op de stoel". (Translation: "in the chair"; literally "on the chair".) This spelling of '37 was already explicitly working towards simplification. The official spelling of '47 went even further, and on that occassion, what remained of the case system was dismantled. Now its just a few relics, retained in well-known expressions.
The key issue is that, not at all co-incidentally, the simplification of the language occurred just as ever greater schooling of the lower classes was being introduced. It was a common idea that language schould be accessible to all, and should thus be made comprehensible to the masses. Archaisms and overcomplications were excised for that reason. Ironically, you can probably solve the issue by introducing publi schooling earlier. If you can get that done when the spelling proposed by De Vries & Te Winkel is the absolute standard, and have the education authority adopt the position that it should be the standard spelling taught to all, the basic result will be that it becomes the standard. The whole theory that language needs to be simplified for the masses, after all, is bullshit. The German 'masses' can use their case system just fine. So if you can get the "unsimplified" language introduced to the great mass of the population before the end of the 19th century, this will no doubt prove that the people are fine with using the case system. The process of simplification is derailed now that its motivation is gone, and there you go.
An alternative solution, albeit a less "nice" one, is to somehow prevent or seriously weaken the dea that the masses should be educated at all. If the particulars of language remain an affair for the elite, simplifying it won't be an issue in any case. Quite the contrary, because using the 'correct' form of the language will then serve as a way to identify oneself as a member of that elite.
A third solution, which can also be used to bolster either of the above, is the introduction of a Dutch equivalent to the Académie française at a very early stage (say it's introduced during the French occupation, and then retained by Willem I in 1815). Such an institute would standardise the language before any reform movement gets underway, and the sheer prestige of this standardised form of the Dutch language would form an obstacle to change.
