First, check the water level in the batteries. Low water in the batteries will decrease their capacity.
I don't have a Limited S, so don't know about the solar panels too much (or why you would need both batteries on for the DVSR to work). But if you need both batteries on to make the radio work, that sounds wrong to me. Normally, one battery should be your starting battery (for connecting to the engines) and the other one should be the 'house' battery (for the accessories, radio, lights, etc.). The idea is that when you are floating you run off just the house battery, preserving one battery's charge to start the boat (even if you completely deplete the house battery). Then when the boat is started and charging, both batteries get charged up (that is what the DVSR does). So if you need them both on to run the radio, that kinda defeats the purpose.
What do you have for a radio? Just stock, or do you have an amp or two? Subwoofer? Additional speakers? Any other power drains going on while you are floating?
Also, how long are we talking about here? An hour or like 8 hours? And do you keep your boat on a charger when not in use? Is it a smart charger with multiple banks or just a simple battery maintainer?
Also, the reading of the voltage while the engines is running is skewed. When the engines are running, you are seeing the voltage generated by the stators, not the voltage from the batteries. It is higher than 12v because it is charging the 12v batteries. When you turn off the engines, you get a truer reading of the battery voltage. So you should be seeing 13+v when running and when you turn it off generally it will drop some.