First please ensure that the inserted game supports the Nintendo DSi microphone feature.
Check whether this problem only occurs when playing a certain game or if it occurs with all games. If this only occurs with a particular game verify if it offers a menu option for adjusting the microphone. You can use this option to adjust the sensitivity level for the microphone. (You will find more information on settings options in the respective game manual).
If the malfunction occurs with all games, the Nintendo DSi will need to be returned to Nintendo Australia for inspection/repair.
Perform a Mic Test. Enter the DSi settings menu, select page 3 and then select Mic Test. The test is performed by speaking directly into the microphone and confirming that the volume bar fills up with coloured bars. If this occurs during the test the microphone is working correctly.
If this does not occur the unit will need to be returned to Nintendo Australia for inspection/repair.