Why do I sometimes lose trophies after coming second in a race?

The current trophy system uses a variety of factors to determine how many trophies you win or lose, including your position, and your total trophies compared to each of your opponents' trophies. If you lose to a player with fewer trophies than you, it's possible to lose trophies even if you finish in second place.

You can always check out the number of trophies of other racers you're competing with at the start of each match.