There are some people whom Allah has favoured, by always accepting their requests. In the hadith, the Prophet (Saw) said, “many a dishevelled one, covered in dust, clothed in old sheets, turned away from people’s doors;

if he swears by Allah, certainly Allah will fulfil his words.”(At-Tabarani) Allah doesn’t judge a person by their looks, but rather by their hearts. Such a person who is apparently a reject in society, has such a strong connection with Allah that He (Azza wa Jal) fulfils their word and accepts their duaas.
One such man was Uwais Al Qarni. Uwais was praised by the Prophet (Saw), though they never met. He always strove to look after and please his mother and because of this, he sacrificed his chance to meet the Prophet. The Prophet (Saw) told Umar and Ali (ra), “if you can find him, then ask him to intercede and seek forgiveness for you. Then Allah will forgive you.” (Muslim) Uwais was not a man of high status in society, yet Allah accepted his duaa, because of his devotedness to Him, and his kindness towards his mother.
We can also take example from the story of Imam Ahmad and ‘the Baker.’ When the Baker took Imam Ahmad in for the night, Imam Ahmad found that he was constantly making Istighfaar whilst working. Imam Ahmad became intrigued by this and asked about it, to which the baker replied that it had become second nature to do so. Imam Ahmad further asked whether he had experienced any reward from this practice. The baker replied, “No duaa I made, except that it was answered…” Making istighfaar often, increases the chances of your duaas being accepted by Allah. Your sins may be an obstruction to the fulfilment of your duaa, therefore, by asking forgiveness you remove the barrier.
There are more people whose duaa is accepted by Allah. The Prophet (Saw) said, “Three supplications will not be rejected by Allah; the supplication of a parent for his child, the supplication of one who is fasting, and the supplication of a traveller.” (Al-Bayhaqi, At-Tirmithi) I’m sure many of us know the story of Sheikh Adel Al-Kalbani, whose mother prayed for him to become imam of the Haram. This is a position usually reserved for pure blooded Saudis, yet Allah answered her duaa, and her son (Sheikh Adel) was appointed Imam of the Grand Mosque. Duaa is such an important aspect of our life, and we should increase our supplications when we are in a position when it is more likely to be accepted. Whilst a person is fasting, they are striving to please Allah, they are abstaining from things merely for the sake of Allah, thus their duaa will not be rejected. As for one who travels, if he travels for a good purpose, such as to seek knowledge, his duaa is more likely to be accepted, but if he is travelling with the intention of committing sin, he should question his travel.
In another narration, the Prophet (Saw) said, “three men whose supplication is never rejected by Allah; the fasting person until he breaks his fast, the just ruler and one who is oppressed.” A person who is fasting has a great chance of their duaa being accepted, as mentioned earlier. A just ruler because he gives everyone their due rights, and governs by the laws of Allah. The oppressed are unjustly treated, and Allah hears the call of the distressed. Furthermore, the Prophet (Saw) told Muadh about the oppressed, “Beware of the supplication of the oppressed, for there is no veil between it and Allah.” (Bukhari and Muslim) The one who is suffering injustice, if he raises his hands to Allah to retain his rights, Allah will answer his invocation, and Allah is the Most Just.
In addition to all the above, the Prophet (Saw) told us that the duaa of visitors to the sick and visitors to the family of the deceased are more likely to be accepted, “When you visit the dead or the sick, then speak good, because the angels say ‘Ameen’ to whatever you say.” (Muslim) Angels are saying ‘Ameen,’ doesn’t this increase the chances of the duaa being accepted?
Moreover, making duaa for one who is absent as the Prophet (peace be upon him) said, “there is no believing servant who supplicates for his brother in his absence, where the angels do not say, ‘the same be for you.’” (Muslim) So, make a good duaa for your ‘brother’ and you will get the same duaa from the angels.
Allah has made duaa so easy and advantageous to us. Duaa is a powerful tool we have been equipped with. Just as Allah has favoured some times over others, Allah has also favoured some people because of their devotedness and their condition. Remember Allah is Most Just and knows what is best for you. So, if you fall under any of these categories of people, increase in your duaa, and know that Allah will accept it.