No, it isn't normal.
Did this always happen or suddenly start happening?
Do you get a specific error message when you try to play the song after wake? If so, type it in exactly as it appears or take a screenshot.
Is there anything unusual about your setup? Are the music files managed by iTunes or by you, and are they inside your user directory (i.e. in the Music folder) or elsewhere?
Is this the latest iTunes (7.3.2), latest Quicktime (7.2, I think?), and latest OS X (10.4.10)?