You can try filling the tires cold to the recommended pressure and then go thru the "Restarting Tire Pressure Monitor" procedure on page 277 of the manual. I have Hankooks too. I don't think they're leaking but what I'm finding is that the tire pressures, according to the in-tire monitors, show the pressure varying a great deal frequently and it's confusing. Readings from my manual pressure gauge doesn't match the monitors' readings either. I'm in the southwest, so altitude and heat account for some of it.
The surest way to tell is to tank test it for leaks. I had one doing the same thing and it was the valve stem, not the valve core, the rubber stem itself had a crack in it. I also had one on another car that was a hard to find screw that the head had worn off. Tank test uncovered it.
one tire of my original set of Hankooks leaked badly at highway speeds - turned out to be a valve stem that was getting deflected at speed and leaking from there. Hard to track down as it didn't leak when not moving and without the centrifugal force...
I think oh have what we call in the automotive industry a “leaky tire”. Since you have the hankooks I suggest replacing all four with Michelin Defenders; remember you want a 101 or better weight rating.
A contrary opinion: I've had multiple sets of Michelin tires on various trucks and none have lived up to the price premium. Here in the southwest Michelins seem to be especially prone to dry rot, which greatly shortens the useful life of a very expensive set of tires. Also, I suggest that you don't choose or exclude a brand of tires based on the claims of a trial lawyer or a newspaper story.
You never know I certainly received an unwarranted talking to and print out that I didn't have MB recommended brand tires on the van the last time it was in. Pretty sure they even looked up the tires I had and added a note to my file that I was running the "wrong" tires as well. The service person said it at least 3 times. For the record the tires are 225/55r17 101V XL as specified on page 291 of the owners manual. It's not the first time I've had my dealer telling me the wrong thing. It took me 2 days of back and forth before they actually looked up and decided that there actually was a 30k transmission service on the van. Next nearest dealer is an hour a way.