We have an exterior GFI outlet that started continually tripping and then quit altogether. We installed a new one but it also is tripping frequently. Anyone have any suggestions please.

Is this GFI the end of the circuit, or does it protect other outlets? Other outlets are being protected if a set of wires are connected to the "LOAD" terminals.

If the end of the circuit, and nothing is plugged into it, there should be no reason to trip.

Be sure the input wires are connected to LINE, black to brass, and white to silver.

It is possible the new device is also defective.

You mention it is used in an exterior outlet - that GFI likely protects other exterior outlets (if present). Try using the "test" feature on your GFI to trip it off and see what other outlets are affected. Are any of the affected outlets (including the GFI) exposed to moisture? Moisture in any outlet of the protected line can cause repeated trips. Make sure all exterior outlets are protected with good quality exterior (covered) outlet plates and caulk any gaps between the coverplate and the exterior wall.

Definitely, as jgj6331 said, check for water. I had the same problem that turned out to be a cracked "in use" waterproof cover. I replaced the cover and the GFI hasen't tripped since.

You have to determine if the load that is plugged in is creating ground current. Some loads produce ground current (like heat tracing or long extension cords, cords with cracks). Even some old equipment may also produce ground current. Since ground current trips GFIC's, that's were I would look first.