Is al-istihlal a condition for the suicide to be damned to Hell forever, or are there other reasons?

The madhhab (school of thought) of Ahl al-Sunnah is that the perpetrator of a major sin—such as one who takes his own life—is under the will of Allah. If He wills, He will punish him; and if He wills, He will forgive him by His grace. He will not remain in Hell eternally unless he deems the sin permissible. There are texts whose apparent meaning indicates the eternal damnation of one who commits suicide, as a deterrent and warning, such as the Prophet’s (peace be upon him) saying: "He who throws himself from a mountain and kills himself will be in the Fire of Hell, throwing himself down therein eternally and forever; and he who drinks poison and kills himself will have poison in his hand and drink it in the Fire of Hell, eternally and forever; and he who kills himself with an iron weapon will have his iron weapon in his hand and thrust it into his belly in the Fire of Hell, eternally and forever." (Agreed upon). However, eternal damnation only occurs if one deems the major sin permissible.