Madman, your advice solved the problem on my wife's phone. It would go to voice mail very often, seemingly for no reason. When I'd call again, it would go through. The reason was simple:
Do not disturb was set to manual, "scheduled" was off and "repeated calls" was set on. Whenever the phone was in standby mode (i.e., locked), the first call received would go to voice mail. If you called again within 3 minutes from the same number, the "repeated call" function would let it through, making it completely confusing.
Verizon Wireless had me do all the network reset business, which did nothing to solve the problem, although when she called to verify if it worked, the call went through since the phone was not locked. Later, I tried (when the phone was locked) and it went to voice mail. So, I tried again (within 3 minutes) and the call went through, completely confusing me...until I read your post!
Tomorrow, Verizon is calling back to see how it's working, and I'll be happy to teach her what the issue was, and will ask her to do her best to spread the word throughout Verizon that it is this iPhone feature that is causing the problem of calls intermittently going to voice mail. Thanks for taking the time to post the solution!