You may need to check the battery fluids... Staying on 13.4-13.6 VDC for long periods of time may boil out your battery fluids and the batteries will then start getting warm to hot just before they die...
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I gave up health foods... at my age I need all the preservatives I can get.
If you have AGM's, 13.4 is the float voltage for Lifelines and you're right on target. Same would apply to wet batteries, the voltage settings are close.