I thought locked rotors is a problem and just a one time issue at that
LRA or Locked Rotor Amperage will happen every time you start the unit. Its equivalent to surge wattage.
For example my well pump has a FLA (Full Load Amperage) of 5.0a
a SFA (Service Factor Amperage) of 6.2
and a LRA (Locked Rotor Amperage) of 18.0a.
So essentially the surge wattage needed to run it is 3x the running wattage.
Motors and Pumps are notorious for needing a much higher surge wattage rating on an inverter to start them.
The same is true for anything with a compressor - refrigerator, freezer, or AC.
I've seen reports of locked rotor amps for these units at well over 50 amps at 120v. Do the math and you are over 500 amps for 12 volt.
50a * 120v = 6000w
6000w / 12.8v = 468a
You say that the batteries should be able to handle 400a, but you are pulling more than that.
Q-Dog says "well over 50a" and even with the 50a equation you are over 400a at the batteries.
Motor-driven appliances (such as refrigerators and air conditioners) for initial start-up require larger amounts of current than when they are running. This is because induction motors initially act like a short-circuited transformer. The maximum start up current is referred to as "Locked Rotor Amps" (LRA) because at the first moment when the rotor is at standstill it appears as if it's locked. This current will drop significantly when motor accelerates to about 75% full speed. The LRA is typically 3 to 8 times continuous operating current (called full load amps, or FLA).
The LRA is typically 3 to 8 times continuous operating current (called full load amps, or FLA).
How to size an emergency generator for air conditioner or motor loads. Running and starting watts of central a/c. How to calculate LRA.
generators.smps.us
So even if we assume the LRA is only 3x what you say the wattage is (1700w) ((not sure if this includes the 500w fan or not))
1700w * 3 = 5100w
5100w / 12.8v =398a
You are simply trying to pull too much from the batteries.
We have done the math in multiple ways.
Its very unlikely its an issue with the batteries.
The first reply you got says it all
Too much surge for the batteries.
Maybe a 3rd will be enough.
Maybe a 4th.
Soft start is much cheaper.
No way of knowing how many batteries you will need to run the AC without knowing its actual LRA