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.
2014 25' Flying Cloud FB
2015 GMC Sierra Denali 6.6L diesel