I have a Leviton GFI in my bathroom which I happened to test today
with my little 3 prong/3 lamp tester. The socket shows as being wired
correctly (2 yellow lights, no red) but pressing the 'trip' button on
my tester failed to trip the GFI (note when the trip button is
depressed all 3 lights (yellow-yellow-red) light up on the tester).
The test button on the GFI works fine though.

Still figuring that something must be wrong with the GFI, I replaced
it with a new one. The physical wiring is correct and again the tester
shows it is wired correctly. Also, the little green LED on the GFI is
lit presumably showing it is working. But again the trip button failed to
trigger the GFI even though again the manual test button on the GFI
worked.

My GFI tester worked fine triggering the other 13 or so GFI's in my house.

Any idea what could be happening here?
Why would both the old and new GFI show as being wired correctly and
yet fail to trip?

I am stumped...