Circuit breakers are more often than not certified to open a fault at its maximum rating (AIC) exactly once in its lifetime, at which time it is recommended to be returned to the manufacturer for recalibration and testing. That said breakers frequently can open large faults more than once, however manufacturers are not required to guarantee this.
Often a breaker that has tripped multiple times does so under an overload (not short circuit or ground fault) condition. If this happens several times in a short duration, such as a matter of hours, the temperature of the internal components can become very high. If you've ever had experience with a breaker which under excessive load trips after a few minutes, is reset immediately and placed under the same load trips within maybe a minute, then seconds, and then possibly will not reset at all until a period of time has passed, then you may have noticed that such a breaker will permanently become more prone to trip. From my experience this is the most common cause of a "weak" breaker. Less often a breaker will be closed into a bolted or arcing fault condition repeatedly, which can lead to internal contacts actually blowing apart or possibly even welding; once again this sort of use goes far beyond what a manufacturer is going to stand behind as accepted use and can actually lead to dangerous and catastrophic failure of a breaker when it can no longer contain the arcing happening within causing it to completely destroy its internal mechanisms or even rupture its outer casing.
The subject gets more complicated when factors such as HACR, SWD, HID and other specialized ratings of breakers are taken into account as all these classes are made to withstand higher than normal temperature and operating conditions. In the case of refrigeration equipment such as an air conditioner a HACR rated breaker is required, it can take the high inrush conditions of starting such a load without damage over time. Nearly all (probably all) currently produced breakers are HACR rated. With circuit breakers you pretty much get what you pay for and a more expensive breaker is more likely to operate better for a longer period of time than the cheapest thing on the shelf.
Finally there is the possible situation of older breakers in a situation where the utility serving said breakers has upgraded its own distribution systems, leading to higher available fault current than may have existed when the original installation was done. Say a thirty or forty year old breaker panel was installed on a system where no more than a 5K amp interrupting current, or AIC rating was required due to line lengths, inefficient transformers or many other factors. Decades later the utility grew sick of their inefficient distribution transformers wasting electricity and upgraded their system. This is all well and good except with this they now require a 22K AIC rating on any new systems. That 22K refers to 22000, yes thousand, amps available under a worst case bolted fault condition. This is a big difference from the 5000 amps those thirty year old breakers were designed to survive and can once again lead to catastrophic failure, ie explosion. Utilities aren't required to make sure their customers existing distribution systems can survive an upgrade in fault current availability, so if you have fairly old breakers it might be wise from a safety standpoint to have a knowledgeable person survey your electrical system and identify any possible risks such as these.
The bottom line is if you think something might pose a problem when it comes to electrical equipment like breakers the best thing to do is have it checked out by someone with training and experience in the field, your electrician should be obviously fairly knowledgeable on the subject and it is often a good idea to weight their opinions higher than say the guy at a hardware store or even a maintenance person who doesn't have considerable experience or training in all things electrical.
Sorry for the long winded response however as many things electrical go there are often few simple, general answers to anything. When in doubt, call an electrician, and if you suspect the answer you get, call a different one. Leave it to the pros!