What is the wisdom behind the delay in the answer to prayer, considering that some people supplicate and prolong their requests, yet see no effect from that, which may cause satanic whispers and ill thoughts about Allah?

The delay in the answer to a supplication has wisdoms and secrets, among them: that Allah, the Sovereign of the Kingdom, does what He wills, and that He possesses ultimate wisdom in His giving and withholding, and that the fulfillment of a request might be a trial for the supplicant, and that Allah's choice for His servant is better than the servant's choice for himself. Furthermore, the delay in the answer might be a reason for the servant to re-examine himself, or because Allah wishes to defer the reward and recompense for him until the Day of Judgment, or to avert from him an evil equivalent to his supplication. The fruit of supplication is always guaranteed: either the supplication is answered promptly, or Allah stores it for him in the Hereafter, or He averts from him an evil equivalent to it.