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.
It is not permissible to ask Allaah's forgiveness or supplicate for the one who dies believing in something other than Islam while the call of Islam has reached him. That is because of the explicit prohibition of this act in the Book of Allaah The Almighty, i.e. His saying: {It is not for the Prophet and those who have believed to ask forgiveness for the polytheists, even if they were relatives, after it has become clear to them that they are companions of Hellfire.}[Quran 9:113]
For more benefit, please refer to Fataawa 14165 and 18298.
As for the one who dies on polytheism and the call of Islam has not reached him or has reached him but in a way that cannot establish evidence against him, he will be tested on the Day of Resurrection as it was stated in some Ahaadeeth. For more benefit, please refer to Fataawa 85624 and 3191.
However, in the worldly life he will be treated as a disbeliever. But, is it permissible to supplicate Allaah to make him stand firm (on the Day of Resurrection)? Actually, we do not know of any scholar who said so.
Allaah Knows best.