I've already added the use of OnKeyDown. I press the keyboard upon startup of the dialog but this function is never entered. That what made me suspect the focus issue from the first place.
Then I added the OnSetFocus and OnKillFocus to try and take a deeper look into this issue, and I saw that the dialog does get the focus on startup (OnSetFocus is entered), but is then stripped away from it (OnKillFocus is entered).