Dua(supplication) is a fundamental aspect of Muslim prayer. People are encouraged to make Dua after each prayer, before bed, before starting something challenging, before anything really. There is no confinement or limitation on Dua.
However sometimes when people want something and make Dua for it they find themselves in facing a stale mate as there Duas are not fulfilled in a miraculous instance.
So there are 3 possibilities that can occur after one makes Dua. (For instance, you pray for a new job- an overly simplified example)
1. The Dua will be granted immediately (you get a job offer the following morning)
2. Allah will not accept your Dua in terms of giving you the job, but will lift the hardship that would have resulted from having no income because of that Dua perhaps you would not run out of food.
3. If neither of the prior two occur, then Allah saves the reward from your dua for the day of judgement, where all your unaccepted Duas from the world will be transformed into good deeds.
So making Dua only results in a win win situation and one should always make Dua and never fail to recognise how just, fair and merciful Allah is.