That sounds awfully like a 'network' issue. These things happen from time to time and are usually resolved within hours but if the problem persists, contact your carrier to make them aware of the issue.
I'm having the same issue. It use to happen sporadically but the last 2 days I have not received all my texts or phone calls. AT&T rep said it might be my area. They are putting in a new tower so hopefully it should improve. I power cycled the phone and they refreshed the device on their end but the messages still havent come through 😟 Hoping this fixes the issue.
I had the same problem, just got Iphone 4 yesterday. Calls went to VM and I was prompted to enter VM password which locked me out. Tried a bunch of different things and once got VM password to work, the missed call log was populated and I had 6 missed calls. Very frustrating-was late picking a friend up and they are ****** not believing I had the phone issue. Seems to be resolved, but I haven't powered phone off/on--that's when I was prompted to reenter VM password. Have been able to receive calls since, but we'll see later.