dosn't always charge

Most times when i plug my iphone into my apple wall charger it registers the charge with no problem. But, sometimes it will connect and charge for a short length of time, then will randomly loose it's connection and won't charge. I try to reconnect all connections, and try different outlets ... with no luck. The only way that it will then charge is while plugged into the computer. Then when I try to plug it into the wall charger, it works no problem again. This happens randomly. What is causing this? How can i fix it?