I have two alarms set... one for weekdays and one for the weekend (and keep in mind, this is just through Start > Settings > System > Clocks > Alarm). Neither has ever NOT worked, even if the phone is in standby.
Nevermind the original question about other time software, had I read more thoroughly I would have seen the Spb Time stuff. I've not used that program, but I do know that several of their programs have reported
numerous issues since the Windows Mobile 6.1 update was first release, and Spb while great programs are also slow developers. It is very possibly a bug/conflict with Spb Time, so you might want to check their Spb Time forum for any information there.
Also, there are some other alarm programs, so you might give them a try if giving up Spb Time is not an option.