The reason your duaas are not answered is because you lack conviction. Your example is like that of the person who came to the Messenger of Allaah (sallallaahu alayhi wa sallam) for advice regarding his brother who had loose stools.
Allaah has said there is a cure in honey. He was prescribed honey. He complained that the honey made his brother's stomach worse.
Abu Sa'eed said:
"A man came to the Prophet (sallallaahu alayhi wa sallam) and said: 'My brother is suffering from loose bowels.' He said: 'Let him drink Honey.' So he drank it. Then he came and said: O Messenger of Allah (sallallaahu alayhi wa sallam) ! He has drunk honey, but it has only made him more worse.'
So the Messenger of Allah (sallallaahu alayhi wa sallam) said: ' Let him drink honey.'" He said: "So he drank it. Then he came and said: 'O Messenger of Allah (sallallaahu alayhi wa sallam)! I gave him some more to drink, but it has only made him more worse.'" He said: "The Messenger of Allah (sallallaahu alayhi wa sallam) said:
'Allah has told the truth, and your brother's stomach has lied. Give him honey to drink'.
So he gave him some more honey to drink and he was cured.'"
[Jaami al-Tirmidhi Hadith No. 2082]
The Messengers of Allaah have complete faith and trust in Allaah. Their conviction is at the ultimate level. When Allaah has said that honey is a cure, then it is a cure. Plain and simple.
Once the man understood this and believed it the loose bowels were gone.
The example also highlights a very important principle:
Do not believe what things appear to be when Allaah has said otherwise.
Allaah said honey is a cure. According to the apparent state of the situation it was not working. But when Allaah has said it is a cure then it is a cure. You believe Allaah and not what you see, hear, smell, or taste.
How will you deal with the trial of the Dajjaal who will have things in his hand resembling hell and heaven claiming to be your lord if you always believe in only the apparent things of life?
Conviction. Have complete and utter conviction in what Allaah says.
He says in the Qur'aan He will answer your duaa. Read and memorize it
“And your Lord says, "Call upon Me; I will respond to you….”
It took the duaa of Moses, which he made for the destruction of Pharoah, 40 years to come to be. This is what Ibn Kathiir has written in his Tafsir.
Never lose hope. Never think your duaa will not be answered. Your Lord, Allaah, will deal with you as you believe He will. Believe He will answer your duaa with absolute conviction and He will. Otherwise work on your conviction until it is perfect.
Narrated Abu Huraira:
Allah's Messenger (sallallaahu alayhi wa sallam) said, "Allah said, 'I am to my slave as he thinks of Me, (i.e. I am able to do for him what he thinks I can do for him).
[Sahih al-Bukhari Hadith No. 7505]