A picture of the state of charge display would be helpful. It might be a Magnum, which will show state of charge listed as volts. Batteries going dead is not a good thing. Once they go below 50% charge, they won't fully charge again, assuming they are lead acid batteries. 12.06V is 50% charge. Even if you have two 100-watt solar panels, they won't provide enough power to run everything in the coach. However, it can be a big help, especially in Arizona and when you are not driving it. First I would check the batteries: how old are they, what kind are they, what is their state of charge and how many amp/hours do they hold. You were right to disconnect them when it is sitting. Let me know what you find out about the batteries.
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Greg
2014 25' Flying Cloud FB
2015 GMC Sierra Denali 6.6L diesel
Charlottesville, Virginia
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