DXWaveList.Items.Add; will return a value of where the sound was added. So try this...
FItem := DXWaveList.Items.Add;
DXWaveList.Items[FItem].Wave.LoadFromFile(TheFile);
DXWaveList.Items[FItem].Restore;
DXWaveList.Items[FItem].Play(False);
It also doesn't hurt to Name your items either...
DXWaveList.Items[FItem].Name:='My Sound';
...this makes it easy to manage items...
DXWaveList.Items.Find('My Sound').Wave.LoadFromFile(TheFile);