TPMS keeps going off on a new Mazda 3
 

I purchased a new 2018 Mazda 3 in Aug 2018. It had 18 miles on it. In late November, the TPMS went off. I took it to the dealer's service department and they found 1 tire low on air but no nail. They said it could be from the vehicle sitting on uneven pavement in the lot. Two weeks later, the TPMS went off again. Took it to the same service department. They found all tires at 35 lbs/sq ft. Nothing wrong with the vehicle. They said, in the morning reset the TPMS. I did that. Two weeks later (yesterday), TPMS goes off again. Anyone have experienced this? Can I ask for a new vehicle?

I don't think you will get a new car replacement, Just keep taking it back,
BUT, Keep Records, Times and Dates of when, and were the fault occurs, and when you take it back to Mazda,
and a summary of what they say at the dealers as a record, so you have a comeback.
Or contact Mazda Direct, go to their Facebook Page and PM them.
On another note, as I have not had this problem as I only have 3 x Mazda 3's 2007, 2009 & 2013.
The other option, find someone with a scan tool, and see if there is any error codes in the BCM.
I have one, but chances are, you not in the Bayside Area in Melbourne.
Good Luck