I have only had one calibration failure over two cars and the car tells you if the calibration has failed. If I remember correctly.
I think you only know that calibration has failed because the "Check Tyre Pressure" warning pops up within 30 mins or so of initialisation, as my three recent failed attempts to calibrate the combo of worn and new tyre on same axle confirm. There is no specific message like "Calibration Failed".
I now have two new Goodyears on the front and have initialised and hopefully calibrated (done 30 minutes 25-62mph) successfully. However I am fully expecting further warnings as these two new tyres bed in, or maybe because there are still two 37,000 mile tyres on the rear.
Looking back at my records I see the two false warnings I had on my car when it was new occurred around 3800 miles, after which the system settled down (and only gave genuine warnings after that, until this week with mismatched old and new).