I have been suffering lof MPG's for about a year now. Sometimes as low as 25 MPG, but averaging 35 MPG. I even replaced the auxiliary battery without much of an effect. Last week, the right-rear tire was losing air. When I went to get the tire repaired, I was shown there was a long nail on the inside of the tire, almost into the sidewall. The tire was not repairable, so a replacement had to be ordered. When the new tire was installed, my MPG jumped back to 45 MPG. This does no seem like a possible effect.
Under-pressure tires are softer. Softer sidewalls flex more as the tire rotates. Flexing the sidewall material turns kinetic energy into heat and reduces MPGs. This is why us MPG fanatics keep our tires at 42/40 PSI (or greater, if the tire maximum pressure rating permits it) front/rear.