There was a similar question asked by dsollen on Worldbuilding SE in July, "How long can language drift before it becomes indecipherable, and how to minimize drift?". In my answer I suggested the following factors could hold back language drift: physical isolation, literacy (assuming the written language indicates pronunciation, lack of literacy (if it led to a tradition of memorizing), political continuity, and use as a language of religion or scripture.
Dan Smolinske has already suggested the final factor in his answer. Judging from past history religion is the best bet for preserving a language. But the situation Malandy has described relates to the future, so perhaps history is not a perfect guide.
Assuming the two groups of humans are descended from space travellers who came from Earth, unlike previous people who have undergone technological regression such as the Moriori, the original survivors will come from a literate, technological society with a mental model of scientific progress. They would see from the start that in order to rise again they must preserve knowledge even if they cannot use that knowledge in their current circumstances. A first step towards preserving the knowledge of the survivors would be preserving the language in which that knowledge was expressed.
Possibly the struggle to survive was so desperate that their original aim to keep a reasonable level of technology failed, utterly for the hunter-gatherers, partially for the medieval group. But preserving the language is less demanding of resources, even if you don't have printing. Copying Latin manuscripts kept the knowledge of antiquity alive through the European "Dark Ages" (yes, I know that they weren't as dark as they were portrayed, but let's assume that in this world they were). Assume the medieval group did something similar, not necessarily out of religious conviction but out of an ideology impressed upon them by the first generation after the apocalypse that it was their solemn duty to do so. It's not inevitable that they would forget the original justification. They might well remember exactly why: so that science can one day rise again, and the people may once more have all the wonderful devices their ancestors had. But it's likely they would become rather hazy about how this "science" stuff actually resulted in the medicine and the air-cars.
This ideology could eventually become a fixed tradition that to let your language change is sinful. Perversely this rigidity in language would work against the longed-for rediscovery of science.
I can easily picture how this would work for the medieval group, where an elite remains literate. Seconding Sean Boddy's answer, it looks a lot more doubtful for the other group, unless they are very different from any hunter-gatherer society yet known. The problem is only partly lack of writing materials. Many illiterate societies have had bards or griots who performed great feats of memory, but they were almost always agriculturalists or herders. Cultivation of crops or domesticated animals allows enough of a surplus that you can keep a non-productive bard fed; hunting and gathering only wild food does not, which is why we know almost nothing of the history of humanity before the coming of agriculture.
