One factor to take into account is that appliances that have a mechanical load like AC units, will draw more current if the supply voltage is less than normal. The supply voltage at the device will be lower due to voltage drop in the service feed ( in your case the shore power cord and / plugs and outlets). A too small gauge shore cord or a too long one will add to the drop causing AC units to draw excessive current. That can often lead to motor overheating and damage unless the device has protection circuitry).
The voltage drop is easy to check. Use a multimeter to measure the voltage at the dock receptacle, it should be 115 to 120 volts typically. Now connect your power cord and turn on your loads like the AC. Now measure the voltage at a 120 receptacle on the boat that doesn't have anything plugged in. Compare the voltage to the supply voltage. If more than 4% or about 5 volts, you may be getting into the risky area.
You boat's power panel may also display voltage. If it does checking is easier: Just turn off everything and note the reading. Then turn on the loads and see how much the voltage drops.
It is also possible that the supply voltage at your marina is low during certain times because you and OTHERS are running their AC units. Again, checking voltages at the boat will show that condition
