The exact context is from the fictional account THÉODRED RETREATS TO THE FORDS IN THE 1ST BATTLE OF THE FORDS OF ISEN (bold text by me):
It had been a dim ... morning, but the mists were now rolling back through the Gap ... and away east of the river [Théodred] descried other forces now hasting towards the Fords, though their strength could not be guessed. He at once ordered a retreat. This the Riders, well trained in the manoeuvre, managed in good order and with little further loss; but the enemy was not shaken off or long outdistanced, for the retreat was often delayed, when the rearguard under Grimbold was obliged to turn at bay and drive back the most eager of then-pursuers.
So the target text is interpreted as:
the enemy was not shaken off and the enemy was not long outdistanced
the enemy was neither shaken off nor long outdistanced
Now let's consider the "and" form, but let's also ignore the original context for a moment.
the enemy was not shaken off and long outdistanced
This has a literal interpretation as follows:
the enemy was not shaken off and the enemy was long outdistanced
In what context could that be true? What if the enemy was, in fact, outdistanced, but still not totally shaken off? This might occur if, for example, there was only one path to take out of a mountainous region, and you were making significant headway ahead of your enemy (thus "outdistancing them"), but they were still not "shaken off" because they were still aggressively pursuing you on the same path behind you. Since the two true facts are in opposition with each other, it would be better to join them with "but":
the enemy was not shaken off but was long outdistanced
Or even better:
the enemy was long outdistanced but not shaken off
Or with an emphasis adverb ("totally"):
the enemy was long outdistanced but not totally shaken off [because they were still aggressively in pursuit]
On the other hand, depending on context, one might suspect that your originally proposed "and" form might be poorly worded or semantically incorrect.
Finally, consider another scenario. What if the enemy took a wrong turn? Then we might have:
the enemy was shaken off [because they took a wrong turn] but not long outdistanced [because it was only recent that they did that, and if they turned around they might catch us]