usually it is 50 times. when you insert your card, there will be a screen that shows what car you are using, what type , car name etc. below that, there is a number. that number is how many times you have left till the next car inspection or card re-newal.
if you are tune a, (for eg), and you choose tune b during car inspection, you lose everything you have for tune a and then re-start mods for tune b.
but it is much faster than before as you already have many points. your car usually mods every time you play 1 game. you keep your points. it doesnt go back to 0, and so, your car is still just as fast as before only the body work changes.
