This is the definition of
휴식 from Naver dictionary.
Why is it
하던 일 not
하고 있는 일 in this case?
In this case, I think 하던 일/하는 일/하고 있는 일 will all make sense.
하던 일 makes sense because it was something you were doing up until now.
하는 일 or 하고 있는 일 makes sense if you view this from the point just before you stop: it's something you are doing right now.
So, in this particular situation, I don't think there's any meaningful difference. (But 하고 있는 일 seems a bit verbose, in my opinion. In general, Korean tends to use simple present tense frequently when English would require progressive: "I go to school now" sounds weird if you're on your way to school, but "나 지금 학교 가" is perfectly fine.)
to describe a noun where the action is recalled to have occurred repeatedly in the past, and is continually repeating to the present (or to the time described in the sentence).
With -았/었던, the emphasis is on the action no longer occurring, and so is not the desired meaning in this case, where it is ceasing at the point of the verb 멈추다 occurring.
It is not -고 있는 because the idea of the continuous is (in general) incompatible with the "stopping" of 멈추다. Note that in English, this is easily confused with the structure of
stop -ing; however, the
-ing form is being used as a gerund / verbal noun here, and should not be confused with its use in the continuous verb English construction
to be -ing.