Yes, you can.
Each time you lose a battle, your Trophy count gets reduced.
Trophies are LOST or WON either when you attack other players or when they attack you.
Losing Trophies can also cause you to be demoted in your Arenas. Example: You were in the Flame Arena I, but lost some battles, thus some Trophies, you would be demoted to the Terra Arena II.
In the top 3 Arenas, trophies are reset every 3 weeks to give all players an equal shot at the MASTER OF MASTERS Title to win exclusive top Dragons, other great rewards and of course the glory!
This means that every 3 weeks there will be a new MASTER OF MASTERS, so compete and win that highest honor!