What's with the passenger side tire?

I would suggest that it is either coincidence, or something to do with the distribution of road debris in your area. When I have experienced such things, they haven't been preferentially located in any particular corner.

If anything, slow leaks from small pieces of not-yet-detected road debris have preferred my rear tires, as if they catch still-tumbling items kicked up by the fronts. The fronts seem more likely to encounter debris flat and settled and not in puncturing position.

 

Obviously, it has some sort of a leak. Might be as @fuzzy1 described. Or it could be leaking at the valve stem, either the schrader valve or between the valve stem and the wheel. Or there could be some debris in the tire seat between the rim and the tire bead. Take off the wheel so you can see all of it and start spraying water with a small amount of soap all over it. Look for the bubbles.

 

Do you check your tire pressures personally or have it done? I find that most if not close to all get them off, meaning they aren't equal side to side nor to spec. I also try to check before the sun comes out to heat up the tires. So depending on the orientation when parked outside if you are checking when the sun has time to heat up one side or corner this can also skew the air pressure.

 

What do you consider "really low"? 1,2,5,10 psi?

"All the tires had good psi except the front, with the front right being real low."

There are only 4. Unless you include the spare.
Inspect the tires closely. You might find a nail, or screw, or other object in the tire.
Spray the tire with soapy water, you might see air bubbles.

If you have a kiddy pool, or large tub you can submerce the wheel in that and you'll probably
find the leak.

There would only be a 1-2 psi difference in the tires on the sunny side.

 

Do you get your tires rotated? If so, and you bring all of the tires up to proper pressure, it would be interesting, and to me really weird, if the newly placed front passenger tire loses air.

I have never had this issue in my 2010 Prius (or any other vehicle).

 

Scuffing a curb when parking?

 

Do you normally check the pressures when ONLY that right front wheel has been exposed to the sun for a LONG time ??
If so, you aren't putting enough air into it........maybe.

It is all "maybe" because there is no design reason for that to happen.

 

When I have a tire that loses air over time, I carefully inspect it with soapy water (Dawn dish soap) in a spray bottle. This will detect the smallest of leaks. I think it’s pure coincidence that you have 2 cars with leaks in the same tire position.^^^

 

This. If it's happening on multiple vehicles I would be looking more at the drivers then the cars themselves.

 

@nudriver :Toyota recommends simple front to back rotation, not side to side as well. How about Hyundai?

At any rate: are both vehicles only front to back rotation, or side to side also?

 

This is not because of the vehicle.
It IS because that most all passenger car TIRES these days have a "directional" design, mostly in the tread to shed water better but sometimes in the belts too.
Switching sides defeats that design purpose.
So does putting them on the wrong side when new.

 

They do?

I seem to be batting 0.000 on this. None of my recent A/S (a.k.a. 'summer') tires, OEM or replacement, have been marked as directional. That includes two replacement sets purchased this year. Only some of my snow tires have been directional.

 

Not the tire manufacturer, but in the Owner's Manuals. Excerpt from 2010 North American manual, page 441:

 

I was referring to Sam's claim that the tires themselves are directional. Only my snow tires have directional arrows, not any of my current or recent A/S or factory installed tires.

 

FWD pattern was that for my (FWD) '85 Cadillac Sedan de Ville. America's Tire still crosses the back to the front causing switch of sides.

 

BUT the owners manual says what it DOES because a LOT of tires ARE directional.
And putting them on the wrong side CAN be a problem.
Your experience is only that.

 

IF......your tires have directional arrows on the sidewalls, that is NOT a good thing to do.
And you should find a different tire shop.

 

What I find amusing is that my "all season" tires are not direction and surprisingly enough, neither are my snow tires.

 

Topic drift?

I was mainly just wondering if OP is in a habit of keeping tires on the same sides, not cross-rotating. Toyota recommends that, regardless of tires being rotational or non-rotational. If he is keeping tires to one side, that might help explain the air loss.