This happens to us, too. We are on the edge of the coverage zone (Verizon). If I'm in the basement, I will receive texts, but not calls. Every so often, I will get dropped calls at my house and I do a service range test????Not sure exactly the lingo, but I call a number and it seems to help my signal. For us, I started with an LG phone, but the service was bad-had to walk out into my driveway to get a signal. Verizon recommended I get a Motorola or Samsung, because they have better atennas within the phone. I will also have trouble when I'm in a bigger store-certain areas are dead zones.
Talk to AT&T. If you are in a bad coverage zone and you just started your contract, you SHOULD be able to trade out the phone for one that has a better antenna. Or, maybe it was just a fluke- a dead spot where you were. If it keeps happening, definitely talk to AT&T before your 30 days (or whatever that company does) expires.
Good luck!!