iPod Classic alarm has never worker reliably!
"Geniuses" & phone support are clueless and disempowered to do anything about it. Apple doesn't seem to read these posts.
You must restore your iPod to version 1.1.1 then reset your iPod and leave it alone for the alarm to go off. Problem is, resetting will loose any changes you recently made to the alarm. Seems alarm will not play a song if you are on pause. Alarm is not triggering a high level interrupt and playing no matter what is going on. Maybe apple programmer think this is a "feature" that alarm won't play a song if another song is cued.
Please post feedback and tell programmers that alarm still doesn't work in v1.1.1 and we want it to fire off the player list no matter what is going on.
http://www.apple.com/feedback/ipod.html
squeaky wheel gets the grease!