The iPhone, although one of the most versatile smartphones, occasionally has issues with dropping calls. This problem occurs for a few different reasons. Sometimes all the phone needs is a simple reset, but it could require a more professional solution. Take your phone into an Apple Store if you experience ongoing problems.
In some cases, the AT&T network simply cannot handle the number of calls coming from iPhones in a given region, because there are too many users. As the Associated Press noted in 2009, "In some big cities, notably New York and San Francisco, AT&T's data network is struggling to keep up." AT&T is continually working to expand its network and fix this problem.
Kinks in Software
Often, updates to the iPhone have a lot of kinks to work out, which can result in dropped calls. The update in 2008 was particularly known for dropping calls. IPhone version 1.13 had many issues with dropping calls as little as a minute into a conversation. This was marked by the iPhone call signal going down to zero bars and then saying "call failed." Once the call ended, the signal would go back up to full strength. Each update to the iPhone smooths out as many of these kinks as possible.
When it first came out in June 2010, the iPhone 4 soon became notorious for dropping calls. It turned out that when gripped tightly, the iPhone's signal strength went down to one or zero bars, thus dropping the call. Even holding the phone left-handed can get in the way of the iPhone's internal antennas. Apple warned users of the problem and soon issued a free protective case to early buyers of the phone, which can be picked up in the Apple Store.
If your iPhone is frequently dropping calls, try a few different options. Try resetting the iPhone by pressing the "home" and and "sleep" buttons for a few seconds, and try resetting network settings in the settings section of your iPhone. Reset the SIM card (on the top of your phone) by pressing it down, which can resolve signal issues. You can also buy a signal booster like zBoost. If these fixes fail, take your iPhone into your local Apple Store Genius Bar and ask for advice. The Geeks there might have specific advice for you, or you can exchange your phone for a new unit if your phone is still under warranty.