There are at least a couple of reasons why "the year is coming to an end" is the idiomatic choice. Firstly, "an end" better describes to the process or generality of something concluding, rather than pointing to a specific, singular conclusion.
articles - The year is coming to an end or the end? - English Language ...
Do native speakers use present continuous when talking about timetables? Can I use "is coming" in my sentence? That film comes/is coming to the local cinema next week. Do you want to see...
Further to Peter's comprehensive answer "Do you come here often?" completes the question in a continuous form, as opposed to the more obviously present "Are you coming?" "Do you come with me?" is certainly archaic and if it was used today it would seem strange, but at a guess it sounded comfortable for about 1,000 years until early Victorian dates.
present tense - Do you come? Are you coming? - English Language ...
If a person is supposed to come but not showing up for the last two days, then which sentence is grammatically correct: He has not been coming for the last two days. or He is not coming for the...
In that sense, when you think about dropping someone off on your way home, you would use "coming" and "going" based on whether the two of your are travelling to or from a place.
grammar - When to use "was coming" or "would come"? - English Language ...