Breakers operate thermally. Bi metallic. New breakers operate correctly. Old breakers will operate from like-new performance to tripping at much lower amperage rating.
Diagnosing with an ammeter is the only way to handle this. First though I would remove the load wire from the 20-amp breaker and insure the copper is not dull and has not annealed from thermal cycling over the years. If the wire was found to be clean and bright then the breaker needs further examination. I would watch the ammeter for signs it is creeping up in amperage as the minutes pass. If amperage is increasing and passes 20 then the blame can fall on the A./C. compressor or motor. If the amperage does not creep upward yet the breaker trips then the breaker itself becomes suspect.
Looking at your profile you have been a forum member long enough to have had an opportunity to see the caution adnd check for loose set screws in your breaker box. Have you don that?
