Finally solved this problem for my phone. Turns out when you take a picture, it affects the Alarm Sound volume. If you take a picture (using the pre-installed Camera app) when the Ringer Volume is on vibrate or mute, it will turn the Alarm Volume to mute. If you take a picture when the Ringer Volume is at some audible level, it will turn the Alarm Volume down. No wonder it seemed random.
Now, whenever I set an alarm, I go to Alarm Sound & then press the volume keys on the left side of the phone to make sure the Alarm Volume is set to max.
To review, for those who haven't read this entire thread, the problem is that when an alarm is set (using the pre-installed app Clock, then going to Alarm), it often works fine but then seemingly randomly, it stops working. In this case, at the alarm time, the screen shows the alarm has activated & the track ball flashes, but there is no sound.
I'm told by HTC that this will be fixed in OS 2.1 (but they don't know when it's coming out).