Breakers can go bad, though somewhat unlikely.
I would look at the ground connection from your alternator. The alternator is bolted to the engine alternator bracket, and obtains a ground there. PlanePower suggests installing a ground strap from the alternator casing to the engine casing.
It is recommended to have the alternator field on when starting (minimizes current surges in the alternator). If the alternator field is off, and the filed breaker (5A) trips .... there's something wrong with your wiring or the breaker. The field breaker should not be popping.
If on the other hand, you are referring to the alternator output breaker (60A), that could be caused by flaky wiring or ground. I would check the ground strap, and make sure your wiring lugs and bolts are all tight and in good shape.
On my 60A alternator, I have an 80A fuse. This is to protect wiring/battery from an internal alternator short to ground (damaged rectifier). If you have a breaker, 60A should be adequate.
Having said the above, you may want to clarify your statement as to which breaker trips, and when it trips (once running at full power, on startup, full load, no loads etc).