from what you just explained about the batteries tells me that the batteries may be either bleeding through the case, or there are cell's failing and causing some voltage irregularities in the system that the controllers are picking up on causing the errors to trigger.
Since changing out the batteries fixes the issues your beef should be with the battery companies.

in these systems they do utilize low voltage in the control circuits so when there are fluctuations they are more sensitive to that change, there is little room for much fluctuation since their parameters depend on a more consistent voltage to operate in the parameters the controllers expect to see in a normal operation. Most newer control sensors use a 5v or 12v signal now unlike the older systems that usually operated off the battery voltage signal whatever it may be on the truck so their range or operation voltage wise was alot wider unlike today's components.

if you continue to keep seeing these battery issues i would tend to start looking at maybe a different battery mfg.

as far as the modules the Mod 1 is the SICOS control and module 2 is the AC3.

Now i do have a service gram that cat distributed and i can send that to you which will explain this problem in more detail and give you some troubleshooting and remedies. It does mention the battery problem and also recommends some checks and possible part replacements that should help.
Do you have an email address you can post in your profile here so i can send this to you?