Is someone who despaired of life and started praying without recourse to supplication because God did not relieve his distress considered a disbeliever?

Supplication (Du'a) is one of the greatest and most fundamental acts of worship. Allah has commanded us to supplicate Him and promised to answer. Allah Almighty says: "And your Lord says, 'Call upon Me; I will respond to you'," and "And when My servants ask you concerning Me, then I am indeed near. I respond to the invocation of the supplicant when he calls upon Me." So, when a Muslim supplicates with sincerity, either he is answered immediately or later, or he is granted reward in the Hereafter, or evil is averted from him. However, one must beware of being impatient and abandoning supplication, for the Prophet (peace be upon him) said: "The supplication of any one of you will be granted as long as he does not supplicate for a sin or for the severing of kinship ties, and as long as he is not impatient." Therefore, a Muslim should not abandon supplication and recourse to Allah, even if he despairs of his life, because supplication brings nothing but good.