Had this happen once with a 2008 Altima... Took it to Discount Tire and they had a mechanism that they ran next to the valve stem to reset them... No amount of driving would turn it off, but their little machine did... They said there might be some corrosion on the sensor from moisture (they said it could have happened from a flat... Or maybe airing down in this case)... When I went in to rotate the tires a few months later, I had them check the sensors and sure enough, there was corrosion on that one sensor... at least that's what I was told.
I think all systems generally take a few miles to go on or off. Prior to getting my Jeep this year, I had a 2008 Honda Fit. The car was awful in the snow, so I ran dedicated winter tires on aftermarket rims. I was too cheap to get a second set of TPMS sensors, so I just dealt with the light being on for four months a year. When I put on the winter rims, the error light would come on, but not for about five miles. When I swapped back in the spring, it would take about another five miles to go off again.
In general, I've found that it resets quicker if the jeep is off while I air up.
Also, I've had luck running at 32 psi with no TPMS light on, so I don't think the pressure needs to be set to man specs. But do make them all very close to the same, even the spare.
2012 JKUR, LOD Mid Width Front Bumper
Warn M8000 winch, Modified stock Rubicon sliders
Teraflex 2.5" coil lift, Pull Pal
FJ Cruiser roof mod (painted white)