Since somebody got my attention...
First and foremost... clean those damn batteries. Get as much off as you can with a dry rag or brush and then wipe them off with a slightly damp towel/rag/etc.
Unfortunately, these are poor batteries for this application. These are basically backup power batteries, i.e., batteries designed to be floated for very long periods of time between uses. When used, they provide backup power at a very high current while another power source comes on line like a generator.
It's very hard to say what needs to be done. There's a reason they only give a float voltage of 13.5-13.8 as that's the way they should be charged. These batteries are not designed for regular cycling. They likely have a very poor cycle life.
Please see if you can find the absorption time. The default is 180 minutes per the manual.
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EDIT: in re-reading some bits of this thread and the manual, I'm sure there's more going on than this. I don't see that this is necessarily related to the fault. Need more information on the fault.
More importantly than all of the the above, which only applies for AC charging, I'd like to see the SOLAR charge controller values.