My left brake light stops flashing when I break. I changed the bulb but it keeps doing the same thing. What could it be ?

did you put right light bulb?

You mean, the L turn signal stops flashing when you brake?  A mean feat to even see the Rear  lamps. and still  be able to push brake without some sort of mirror or assistant.  Does the brake affect the front  lamp as well?

Investigate the sockets  and ground wires on left side, rear. An open ground can make things act like they are possessed, grounds finding their way thru other loads.

Your left brake light stops flashing??? 

I don't understand...

Check all the lights, not just that one..

Unless your turn signals use the brake light bulb when turning the brake light should not be flashing.

Check for power and ground at the connection with a test light with the brake pedal pressed.

a loose/rusted ground wire ??