Salam,
How many a dua is uttered as a routine with little focus or attention? I find this with the dua after the prayer which is often offered as a ritual formality. Compare this with the times when you feel a special connection and closeness when making your dua, this is the ideal scenario (may God grant us this always, amin). This latter state – a special feeling of closeness – was regarded by some of the early Muslims as being an indicator that this is a time when duas are accepted. The following incident involves the great Tabiee (student of a companion) Saeed bin Jubair:
Dawud bin Abi Hind said: when Hajjaj arrested Saeed bin Jubair, Saeed said to Hajjaj: I only see myself being killed, however I want to tell you: I was one day supplicating with two friends of mine-at a time when we noticed a special feeling in our dua, and we all asked Allah for martyrdom. Both of my friends have attained it, and I am awaiting it.
Siyar – Fawaid 1/153
Dawud bin Abi Hind said: It is as if he was of the view that duas are answered when you have a special feeling [of closeness].
