Is the requirement for offering the fixed Sunnah prayers removed during travel, and (if so) what is the evidence for this?
It is prescribed for one to leave the fixed Sunnah prayers during travel, except Witr and the Sunnah of Fajr. It has been authentically reported from the Prophet (sallallaahu alaihi wa sallam) in the Hadith of Ibn Umar and others, that the Prophet would not pray the fixed Sunnah prayers while travelling, except Witr and the Sunnah of Fajr.
As for the supererogatory prayer, they are prescribed during travel and while one is resident, and likewise the prayers for whose performance there is a reason, such as the Sunnah of Wudhu, Tawaf, Adh-Dhuha, and Tahajjud prayer at night, based upon Hadiths which have been narrated to that effect. And Allaah is the Granter of success.
Shaykh `Abdul-`Azeez Bin Baz
Fatawa Islamiyah Vol. 2 Page 431
Darussalam English Publication