This website lists about two dozen three-word phrasal verbs. As I looked through the list, they all seemed "inseparable" to me.
However, have said that, I think there is some wiggle room for a few of these, due to the flexibility of prepositions.
For example, consider talk back to. That form may be the preferred version, but one might see talk back at used instead:
When you're in school, don't talk back at your teacher.
Also, there are times when one of the three words can be cut out altogether, resulting in the use a two-word phrasal verb instead. For example, the website lists check up on as a phrasal verb meaning "examine" or "investigate," with the example:
The boys promised to check up on the condition of the summer house from time to time.
I think one could remove the up and retain the same general meaning:
The boys promised to check on the condition of the summer house from time to time.
As for your example, the preposition could probably changed from on to with, and the result would be a more common way of writing it:
Unfortunately, I wasn't able to keep up with the news while I was away on vacation.
Best Answer
Separable phrasal verbs are the ones that can take direct objects (transitive). Direct objects in the second example is my book and it.
While inseparable phrasal verbs are the ones that cannot take direct objects (intransitive). That would be the first example.
In your question, the first example seems right to me.
In the set of the second example, that would be separable phrasal verbs that have direct objects (my book and it). Take a look at this rule for separating multi-word phrasal verbs.
So, the first three sentences are in correct English. Although I sense that the third sentence sounds a bit weird to me. But it's still grammatically right based on the link I provide you and this additional one.
Meanwhile, the fourth sentence is literally wrong, since it has a pronoun (the it) that always comes between the verb (get) and the particle (back+from).
So, I summarize the correct examples for you [Better in past tense anyway]: