In Quran, it is stated that there are responds to every supplication. Yet most of our supplications are not accepted favorably?
Bediuzzaman (author of Risale-i Nur Collection) explains the issue as follows:
If you say: We frequently offer supplications, but they are not accepted. However, the verse is general; it states that every supplication is answered.
The Answer: To answer is one thing; to accept is something quite different. Every supplication is answered, but its being accepted and exactly what was sought being given is dependent on Almighty Gods wisdom. For example, if a sick child calls the doctor, saying, Doctor! Doctor!, and he replies, Here I am, what do you want?, and the child says, Give me that medicine! the doctor will either give him exactly what he asks for or something better and more beneficial for him. Or knowing that medicine is harmful for his illness, he will give him nothing.
Thus, since Almighty God is all-Present and all-Seeing, He responds to the supplications of His servants. Through His presence and response, He transforms the desolation of loneliness and solitude into familiarity. But He does this, not in accordance with mans capricious and importunate demands, but in accordance with the requirements of dominical wisdom; He gives either what is sought or what is better than it, or He gives nothing at all. (1)
Besides there are some Hadiths that highlight this issue. One regarding this point was reported by Abu Hurayra. The Prophet Muhammad told:
Your every supplication will be answered if you be patient. There are some who complain, I offered my prayers, but they were not answered. Another report by Muslim is as follows: Unless one of you demands sin or cut-off of kinship from Allah Almighty, your supplications continue to be accepted favorably. Again Tirmidhi reports, He whosoever offers his prayers to Allah Almighty, his prayers will be answered. It will be either accepted in the world or in the hereafter; or through this prayer, his sins will be decreased save he demands sin or cut-off of kinship or be in impatience. (2)
As is clear from the Hadith, mans supplications are accepted unless s/he demands sinful or religiously prohibited things.
(1) The Words / Twenty-Third Word - First Chapter - p.325
(2) Bukharî, Daavat, 22