What was the current draw on each of the two legs with both air conditioners running? Without knowing that, it's impossible to say with any real certainty if the breaker was working properly or not.
Standard breakers operate thermally (for the most part--for very high current overloads, such as a dead short, they have a magnetic trip mechanism that acts more quickly). The average current being consumed is measured by how much it heats up a little bimetalic strip, and if it heats up and bends enough it causes the breaker to trip. Anything that makes it heat up more will cause the breaker to trip earlier--higher temperatures in the box than expected, poor contact between the breaker and the bus bars it's mounted on, or I presume poor contact internally in its contacts due to repeated tripping/disconnecting under load.
My guess is that the breaker is in need of replacement, but without actual measurements of stuff it's nothing more than a guess.