Is it permissible to inform the parents of an atheist friend about his atheism after numerous failed attempts to guide him [to Islam], and what is the correct course of action in this situation?

Your friend is in grave danger unless he repents and returns to Islam. You must continue striving for his repentance without despair, for enjoining what is right and forbidding what is wrong is emphasized for those who know it. The command to enjoin good and forbid evil does not cease due to a presumption of no benefit; rather, it must be done. There is no harm in gently informing his parents, for their prayers are answered, especially the father's prayer in the unseen.