FWIW, in the USA, there's a reason why they specify use of a 40A CB on a 32A EVSE. NOw, you can build them with different curves, but even then, pulling nearly max over time is just not reliable. Most require a constant overload for a period of time before they'll trip. They'll trip nearly instantaneously only if the load is exceeded, often by a considerable amount. Each of those factors can be tailored for specific applications, but again, essentially a 32A load on a 32A protection device IMHO, SHOULD trip after an extended time, especially as there are slight voltage variations, the load won't be able to react instantly, and the actual current draw could fluctuate slightly. Most meters probably wouldn't be able to show that as their sample rates aren't that fast, but if the CB was on the edge, it could just be enough to cause it to trip when one happens.
Typically what will happen as the wire heats up is that its resistance will rise, which will drop the voltage at the load. Dropping the voltage will drop the power available, even at the same amperage draw. Since power = volts * amps, you'll charge at a slightly lower rate, even as the amps stays the same. It is the pilot signal output of the EVSE that the car reads to determine the maximum current draw it can apply to the EVSE. If that is stable, the current level the car pulls should remain stable, and as voltage changes, the actual power delivered will change.