Originally Posted by joecaption
One loose connection is going to cause a GFI to trip.
Since it works OK on the GFI outlet, but not on the 2nd and on down the line, it sounds like the problem would be somewhere from the "load" connection on the GFI to the 2nd socket (the 1st socket down stream from the GFI).
In the workbox for the 2nd outlet, you could disconnect the wires leading to the 3rd outlet, but leave all the rest connected. If you still have the problem, you've isolated it to GFI --> Outlet-2. If the problem disappears, then it's downstream of outlet-2.