@WatsonB How odd! Have you had a go at clearing the cache and data of the Clock app? Just head to Settings > Apps > Clock > Storage > Clear cache/data to do this.
@WatsonB: Have you noticed if the icon disappears from your Status Bar under any specific conditions? Have you tried deleting your current alarm via the Clock app > Alarm > Press and hold on the alarm > Delete all, then re-adding it to see if this helps?