Is it permissible for a worshipper to perform the prayer without raising his hands during prayer at all?

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.

If a worshipper does not raise his hands with every Takbeer during the prayer, this does not invalidate his prayer. However, the worshipper who fails to raise his hands will miss great rewards. Raising the hands during the Takbeer in prayer is reported in Mutawaatir (i.e. collectively contiguous) narrations on the authority of twenty-one Companions . ‘Abdullaah ibn ‘Umar said, "I saw the Prophet, sallallaahu ‘alayhi wa sallam, raising both his hands up to the level of his shoulders when starting the prayer and upon saying the Takbeer for bowing. And when raising his head from bowing, he used to do the same and then say "Sami‘a Allaahu liman hamidah", and "Rabbana wa laka Al-Hamd." And he did not do this (i.e. raising his hands) in prostration." [Al-Bukhari and Muslim]