My fathers hedge trimmers used to trip the breaker on his outdoor circuit. I replaced his 100+ feet of #16awg cords with #12 and problem solved. :roll:
If this lawn mower motor is not a brush (DC) type motor found in many hand tools, then this would be my first guess, long extension cord tremendous voltage drop leads to pole slippage and very high current, installing a bigger breaker will only allow the motor to fail sooner, at rated 12 amps it should not be tripping a 15 amp breaker, as others pointed out address the problem, not apply a band aid, thats what we get paid for.
A few other questions to ask:
How high is he letting the grass get.
How sharp is he keeping the blade<<<Biggie with electric lawn mowers.
If over load on mower not tripping, then possible bad breaker, or over load that wont trip till much higher.
A 15 amp breaker should hold a 15 amp load for ever.