The breaker may be weak and it could be a poor performing breaker.
BUT, if it actually trips when you shut down the generator (every 5th time), you have to ask yourself how the generator, which produces 120V AC, triggers a problem on your 12V DC system.
One possibility is the generator somehow backfeeding a 12V spike from the generator's starter, back to the battery. But the 80 amp breaker probably isn't in that direct path, so maybe this is a less likely possible cause.
Another possibility is something in the generator shutdown affecting the Power Converter; the Power Converter having 12V DC output that goes directly to your 80 amp breaker. If the Power Converter is producing a spike that trips the breaker, that could trip the breaker, but you have to ask what's causing it to produce a spike when the generator shuts down.
As the generator shuts down, as soon as voltage on the L1 leg drops below 105V, the contactors in the transfer switch actuate.
So, my best theory is that something in the transfer switch operation is causing the Power Converter to generate a spike on the 12V DC output, tripping your 12V DC breaker.
That said, the breakers are usually thermal expansion, driven by excess current. And they usually take at least several seconds of excess current to heat up enough to trip. So a momentary spike might have to be pretty significant, or perhaps the breaker being weak would cause a brief spike to trip it.
A new breaker might get rid of the problem, but might not fix an underlying condition. If you have pitting on the transfer switch contactors, it'll get worse over time and eventually you'll have a high resistance problem at the transfer switch.