Definitely claim and take the service manager out in the car and demonstrate the fault, inducing the fault if you have to.
Don't be deterred by him saying that you are beating the syncro as you are changing too fast or by him saying that it is wear and tear.
If it comes to it, politely argue the case that it is a sports car and quick gear changes are part of the sports car experience.
Also, hold firm on that it is a mechanical failure issue and not wear and tear.
Good luck and keep us posted.