First, you need to understand that your RV's AC unit draws around 6-8 Amps when it is running, but when it first cycles, the Compressor has to start up, and this can add another 3-4 amp temporarily, until it is operating. Your RV breakers and circuitry to the AC are designed to handle this load.
But, as an AC unit ages, it takes more current to get the Compressor running, as much as 6-8 Amps as opposed to the current needed to start a new AC.
So, what you end up with is a load, from the AC unit itself of 8-12 Amps. Or as high as 14-18 Amps for an older unit.
So, if you have other appliances also operating in your RV, you could be near the maximum load of your RV wiring which can cause your overall supply of power to "sag" as this extra load from the AC compressor occurs, which in turn can force your breaker to kick.
Then there are your Circuit breakers. The breakers in your Rv are probably original to the RV, and over time, if they have been "Kicked Off" many times, the metals inside the breaker can become "stressed," and the breaker can start operating at a lower current level. So, simply put your original 15-Amp breaker could be operating at a lower current such as 14-Amps.