Sri U. Ve. Vasudevacharyar Svami, while on the discourse of Kaisika Purna, said that like how Sriramapiran in Ramayana accepted sharanagati of Vibhishana at once, Nambaduvan accepted the sharanagati of the Brahmarakshas straight away. But Svami Desikan has not mentioned this sharanagati in the Abhaya Pradana Saram. What is the reason?

Svami Desikan indicated some of the sharanagati-s as examples in his Abhayapradana saram. He might have mentioned a few sharanagati-s as examples. The others do not become non-existent just because Svami has not mentioned them.
He has primarily highlighted sharanagati involving Perumal, along with the sharanagati-s from Itihasa-s as mentioned by the ancestors.
Nambaduvan Brahmarakshas sharanagati exists. Mentioning only this must be taken as an analogy for other sharanagati-s that exist.