As the title of my question says:
Is there any report that our prophet SAW (PBUH) performed one Wudu' and prayed more than one Salah with it?
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Yes, there are reports that he did that on certain occasions, although he would usually renew his ablution for every salah.
أخبرني سويد بن النعمان، قال: خرجنا مع رسول الله صلى الله عليه وسلم عام خيبر، حتى إذا كنا بالصهباء، صلى لنا رسول الله صلى الله عليه وسلم العصر، فلما صلى دعا بالأطعمة، فلم يؤت إلا بالسويق، فأكلنا وشربنا، ثم قام النبي صلى الله عليه وسلم إلى المغرب، فمضمض، ثم صلى لنا المغرب ولم يتوضأ
Narrated Suwaid bin Nu'man: In the year of the conquest of Khaibar I went with Allah's Messenger ﷺ till we reached Sahba' where Allah's Messenger ﷺ led the 'Asr prayer and asked for food. Nothing but Sawiq was brought and we ate it and drank (water). The Prophet ﷺ got up for Maghrib (prayer), rinsed his mouth with water and then led the prayer without repeating the ablution.
أن النبي صلى الله عليه وسلم صلى الصلوات يوم الفتح بوضوء واحد
The Prophet ﷺ prayed all the prayers on the day of the Conquest (of Makkah) with one Wudu'