Cannot make conference calls on iPhone 4S

When connected to one person, I hit the "+" button, select a contact, and then the iphone indicates it is calling the 2nd person but the 1st person remains audible on the call. After a few seconds, the 2nd call appears to go through because the "merge" button appears as well as the name of the 2nd person I called. However, when I tap the "merge" button, the 2nd caller is not there. When I hang up with the 1st person and call the 2nd person, they tell me they didn't receive the 1st call to them.

Is this a phone problem or user problem?

Thanks,