If a person recites a verse containing a prostration of recitation (sajdat al-tilāwah) multiple times within the same sitting or setting, performing a single prostration is sufficient. However, if a person recites different verses of prostration within the same setting, a separate prostration is required for each distinct verse of prostration.
(al-Kudūrī, Sharḥ Mukhtaṣar al-Karkhī, 2/59)
For example, a person memorizing Sūrat al-ʿAlaq is not required to perform a prostration each time the verse of prostration is recited, as long as they remain in the same setting and continue the recitation; a single prostration suffices for all repetitions. If, however, a person recites Sūrat al-ʿAlaq together with Sūrat al-Inshiqāq, then, since two distinct verses of prostration have been recited, a separate prostration must be performed for each.
The cause of the prostration of recitation is the recitation of a verse that contains it. Accordingly, by analogy (qiyās), repeating the verse would ordinarily necessitate repeating the prostration. However, as an exception to this general principle (istiḥsān), the fact that the Messenger of Allah ﷺ performed the prostration only once despite reciting the same verse multiple times in a single sitting indicates that one prostration is sufficient. This practice provides ease for those who learn, teach, and memorize the Qurʾān.
(See: al-Kudūrī, Sharḥ Mukhtaṣar al-Karkhī, 2/59; ʿAlī al-Qārī, Fatḥ Bāb al-ʿInāyah, 1/383)
This ruling applies on the condition that one does not leave the setting, either physically or legally. Physical departure includes leaving the room in which one is reciting. Legal departure includes actions that interrupt the recitation, such as engaging in conversation, walking, or eating. Scholars have defined the limits of such interruptions as speaking more than three words, taking more than three steps, or eating more than three bites.
In conclusion, if a person repeatedly recites a verse of prostration without changing their position or state, a single prostration of recitation is sufficient.