Turn the power off to that circuit and remove the GFI receptacle. Chances are, there's a loose connection. If not, check the closest outlet from there for a loose connection.
If you can't find a loose connection, make sure the line & load terminals of the GFI are correct. "Line" should be the source of power, "Load" should go to the other outlets. They may be reversed.
If all else fails, check for 120V at the load terminals of the GFI when power is on and the GFI is reset. If there's no power, replace the GFI.