All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His Slave and Messenger.
When reciting the Quran, one is not obliged to continue until the end of the verse or a complete meaning. It is permitted to pause for some hindrance like coughing, running out of breath, and so on. The reciter should not cause himself hardship by continuing the recitation. Allaah says (what means): {….and has not placed upon you in the religion any difficulty.} [Quran 22:78]
In case the reciter pauses and wants to resume the recitation, then he has to resume from a place that is permissible to start from so that the meaning remains correct, and so that there is a connection between the beginning and end of the sequence of words.
As-Suyooti says in his book Al-Itqaan: “An-Nashr by Ibn Al-Jazari reads: 'Since the reciter cannot recite a Soorah or a narrative in one breath, and it is not permissible to breathe between two words in case of Wasl [joining verses/sentences without stopping], as that is like breathing in the course of uttering a single word; then it is obligatory to choose a Waqf [stopping on the last letter of a complete word to read the next one] for breathing and resting, and this makes it obligatory to choose an appropriate starting point; and it is obligatory that the sequence makes sense and does not alter the meaning, as it is through [the meaning that miraculous nature of the Quran resides]; it is for this reason that the Imaams emphasized learning and knowing it [i.e. the science of Waqf].” [End of quote]
The obligation here does not mean the Islamic obligation that renders a person sinful if he does not do it, as Ibn Al-Jazari himself said in his Manthoomah that it is not an obligation:
"And there is no obligatory Waqf in the Quran or a forbidden one except what has a reason (i.e. to be so)."
Allaah Knows best.