If you are running from your house, remember everything that runs through that one breaker in your panel subtracts from the availability of AMPS from the trailer. If you have a lamp inside the house on that same circuit, and it's drawing 5 amps, that leaves only 15 of the 20 for the trailer. So make sure there is nothing else running on that circuit.
Second, you can run your air conditioner all day and night on your current configuration, IF that is the only thing running. It's no different than running a window air conditioner on a long extension cord. BUT, you also have to remember, there is more AMP draw in your camper than what meets the eye.
Water heater on electric? Microwave? AC powered appliances? Electric clocks, phone chargers, everything .... pulls from that original 20 amps.
But, if you watch what you are running on AC power, you CAN run the air conditioner indefinitely. We did it that way for many, many years. We'd get the camper cool at home, then turn the air off so we could enjoy the camper in the evenings and sleep in it at night. But when running the television, or anything else, the air conditioner was always off. 20 AMPS gets used up pretty fast.
We finally installed two 30 amp RV plug at different spots on the property so we can move the trailer around. Now, now problems at all.