if i'm not mistaken, honda uses an indirect tpms system. you do not have a sensor in the spare tire. the indirect system is based on an algorithm that the computer uses to check the rotation of each tire and compare them to one another. if your tire is low on pressure, the rotations will be different than the other tires.
if it's been truly recalibrated...and the all the tires are the same pressure...then, unfortunately, it appears your tpms system is malfunctioning. i'd try another dealer - one who at least knows what they are talking about.
if you have two different tires on the car (read: offset, staggered, etc) your car will throw the tpms sensor and light up the dash.
i had a few issues with mine way back when....over time, it actually fixed itself and hasn't happened. read - some electrical interference COULD cause a malfunction (which is what happened to mine). i'd be driving down the highway...and all of a sudden, my lights would glow. i'd check the tires...and all were good. i'd reset/re-calibrate the system...and it would work for long time....then, it would do it again. after about 1.5 years of this (maybe 3 times in that span) did it happen, it no longer comes on. i'm going on my 3rd year of the car and 65K miles.
hiding from those who might be looking for me