As the respected Sayyid al-Musawi has explained, the person who banned Mut'a was 'Umar b. al-Khattab and not the Prophet (s). However, it is true that many of our Sunni brothers and sisters believe that the practice was abrogated by the Prophet (s) himself. This view is based on some hadith narrations that seem to suggest so.
The notable scholar and Marja' Sayyid al-Khu'i has covered these narrations from the Sunni sources and debunked them in his work Al-Bayan while discussing the topic of abrogation of Qur'anic verses.
You can read the chapter here, the relevant section is to be found after some scrolling, or you can simply search for '4:24'. Hope this helps.