We should not necessarily think of it as like a big conference all the monks were at where they decided which works to save and which to not. A lot of the initial work of manuscript transmission took place in the eighth and ninth century as part of a reform movement to beef up clerical Latin skills, so they were often just saving what texts they had on hand.

That being said, my answer basically just kicks the can down the road, and as long as that caveat is in mind your question is still a useful one. And the answer is, well, often it is a bit opaque. Sometimes we can know why a work was saved: The Aeneid, for example, was the work of Latin literature, so saving it would be like saving Shakespeare, only more so. Ovid was widely regarded as an exemplar of Latin style in the middle ages. Juvenal was popular as a didactic tool to illustrate the moral turpitude of pre-Christian Rome. Seneca was widely regarded as a moral sage.

There are some cases where we can't say much specific but it is possible to imagine a reason. I can imagine an intellectually curious abbot wanting Pliny, the equivalent of the Encyclopedia Britannica. I can see Horace's odes to the bucolic countryside and separation from the bustle of political city life appealing to a monk.

And then there were some texts that were probably saved for impenetrably personal reasons, such as Lucretius, whose text is not only impossibly difficult but also antithetical to Christianity.

This mostly comes from Gantz' Latin Literature.