P0456 means there was a very small evaporative leak detected.
The Hyundai scan tool provides the technician a means to have the vehicle
run the evaporative emissions test. If the test repeatedly reports back
that there are no leaks found, then that means the problem isn't present
at the time the technician is testing the vehicle. In that case you're
probably looking at one of two possibilities. First, the fuel cap could
have been a little loose or crossthreaded, or the tether could have been
caught under the cap gasket. I've seen all of these. Second, the
canister close valve may intermittently not seal properly. This valve
doesn't affect the function of the evaporative system except that the
vehicle cannot properly test the system. The sole purpose of the close
valve is to seal the system so that the computer can apply engine vacuum
and monitor the fuel tank pressure sensor to check whether the system is
leaking. I've also seen a few of these close valves fail in this way.
In most cases, if I run the evap test 10 times and receive no failures,
the car doesn't return with a repeat issue. At this point, I'd recommend
you make sure that the tether doesn't get caught under the fuel cap, that
you don't crossthread the cap in the filler neck, and that you fully
tighten the cap. Then, if you're diligent about this, and the same code
returns, you'll know that the fuel cap installation isn't the issue. In
this case, be sure to represent to the dealer how diligent you were in
making sure the cap was installed correctly.
The close valve is the only moving component in the system which could
cause a small leak, so it's the primary suspect in causing an intermittent
leak. As I recall, though, I did see a few Santa Fes where the screws for
the fuel pump were overtightened and distorted the flange so that it
didn't seal properly. The leak was apparently just the right size so that
the code would only set on 30% of the evap tests or so. But, once again,
running a few successive tests caused a failure to occur.