It looks like you GPS unit is "Wandering." It frequently happens when a GPS loses sight of signals sporadically. It could be the unit or it could be the area where you are running. When a GPS unit is in good condition and you have wandering, it tends to be signal blockage due to foliage, building or other structures. If the GPS unit is bad, you typically see some of the channels that it is tuned in on dropping the signal for a specific satellite and then picking it back up. If it is the first issue, then there isn't much you can do except change where you run. If it is the second issue, the unit is defective.
It is not A-GPS. A-GPS only uses the internet 1 time, when it first tries to achieve a lock. Your phone always uses A-GPS when you have an internet connection. The unit does an extremely rough triangulation based on cell towers or WiFi and sends that location to a site that returns the current satellite positions for that area. I speeds up your initial lock tremendously, but it only does it when you first crank up the GPS unit in the phone.
You can test your phone with something like GPS Status (an app) and watch the individual satellite signals and see if it randomly dropping the strong signals or you can just get AT&T to change your unit out and see if that helps with the issue.
Sorry, didn't mean to write a book, but I hope is helped some.