First, consider installing a battery dedicated solely to starting your
genset. That will be your last line of defense should everything else
aboard discharge.

Your starting batteries may well charge from a different alternator
than your house batteries, and if you have more than one alternator
that is a rather likely scenario.

It sounds like something is preventing your batteries from charging
properly- (usually either the condition of the battery itself or a bad
charging circuit), or is allowing the house bank to discharge
when apparently unused. Check battery condition,
alternator output, connections (very important), and wiring. If the
wires are large enough and properly connected, if the battery is in
good physical shape, and if the alternator is producing ample voltage
it's most likely a short downstream from the battery.

Do you have some fancy regulator, splitter, or combiner in the circuit?
If so, check that as well.