Loss of voltage overnight is expected. All of this assumes the batteries are in top condition and the water levels are checked regularly. As a reminder only add distilled water as the minerals in tap water can destroy a battery. Typically setting your generator to autostart based upon various demand requirements is how to solve the issue. That has several considerations as well. There is a quiet time setting which prohibits autostart as well as settings that adjust the demand requirements.
Autostart will generally run the generator prior to the start of quiet hours to peak the batteries.
On the upgrade side is the option for more robust solar and/or Lithium batteries.