What is the interpretation of unanswered prayer despite the promises of Allah, the Exalted, and does this contradict reliance upon Him, and do such thoughts lead one out of Islam?

A Muslim should first doubt himself and search for the reason why his supplication is not answered, for Allah has promised to respond in His saying: "Call upon Me; I will respond to you." The reality of the response is that Allah responds with what He deems good for the servant, and at the time He determines, and this may be different from what the servant desires, in fulfillment of His saying: "And perhaps you dislike a thing and it is good for you." The forms of response vary: either Allah grants the supplicant what he asked for, or averts evil from him commensurate with it, or stores it for him in the Hereafter, as stated in the noble Hadith. Among the impediments to the answering of supplication is impatience. A Muslim should not say, "I supplicated, but I was not answered," and he should persist in supplication, and supplicate with certainty and a present heart. Whoever does so will not be deprived of one of three things: the answer, or the warding off of evil, or its deferral to the Hereafter.