The portable ac in one room trips the 15 amp circuit breaker after about 45 minutes, can the breaker safely be changed to a 20 amp breaker?
Never. Of course not. If the building had been built with 20A wiring, they would've just used a 20A breaker in the first place. They cost exactly the same as 15A breakers.
Anyway, if the appliance was supplied with a standard 15A plug (parallel prongs, you know the one), then it definitely works on a 15A circuit. UL would not have given it a listing otherwise. In fact, air conditioners typically draw around 4-8 amps, and you've got 15.
The real problem is something else on the circuit.
Or, the "something else" being run at the same time as the air conditioner, and together they are exceeding 15A. You will know where to look for the "something else", because it too loses power when the air conditioner goes.
You cannot go from a 15 amp breaker to a 20 amp breaker unless you confirm the wire feeding the circuit is #12 AWG. The wire installed is probably #14 AWG and it's maximum rated amperage is 15. If you have a ability to replace the wire to #12 AWG, you can replace the breaker to a 20 amp. You would want to then replace the outlet to a 20 amp outlet. What does the name plate for the ac say about amperage for the unit?