Lots of good advice above!
There are many possible reasons for these symptoms.
"When the engine is running or plugged into shore power or the generator is running the batteries appear to be charged up based on the control panel reading - 13.8 to 14.1 volts."
These voltages are the output of the converter/charger (possibly inverter/converter/charger). To fully charge lead acid batteries the charging voltage needs to be applied for 14 to 18 hours. Longer if the batteries have been abused.
"Once the batteries are no longer receiving an outside source of power for charging, the batteries within a couple of hours appear to discharge to a point below 9 volts"
You will need a cheap digital voltmeter. Get one from your local hardware store.
There are multiple possible causes for this. Possibly even multiple contributing causes. To narrow down the possibilities, perform this test.
Fully charge the batteries using shore power for 24 hours.
Disconnect the shore power and monitor the voltage.
Voltage should quickly drop to between 13.0 and 12.7. Possibly 30 minutes.
Determine how long the voltage stays above 11.0 volts. This should take much longer, possibly 12 hours.
Battery capacity vs Power used.
Your battery bank may not be large enough to do the job you want.
What is the amp hour capacity of each of your two batteries?
The capacity may be on the battery labels. You may be able to find it by Googling Brand, Model number.
"This has been a problem almost from the day I purchased the RV."
This indicates the power draw is too high for the battery bank size. It could also mean the batteries were defective from the start. Assuming power draw is too high you may be able to reduce consumption.
A compressor type refrigerator also uses excessive 12 volt power possibly through an inverter. Test to see if this is the problem by switching it "off".
120 volt appliances often use excessive 12 volt power through an inverter. Switch the inverter "off".
"This has been a problem almost from the day I purchased the RV. For the last 5 or 6 months I do turn off the battery disconnect switch when I'm not using the RV"
The key word above is "almost". If they worked on day-one, then the problem is most likely yours.
Lead acid batteries must be stored fully charged. Recharge 14 hours before terminal voltage drops below 12.4 volts. Monitor terminal voltage during storage until you know how long you can go between charges.
Without turning the battery disconnect switch "off" as you did not do for 5 months, you should expect 2 or three days of storage without damaging batteries. A full clean 14 hour charge would be required after two days.
Storing batteries for a couple of weeks at 9.0 volts will cause significant "sulfation". This translates to loss of capacity. The deeper the discharge and the longer the time, the more the damage.
I get 5 days using my 200 amp hour battery bank while dry camping. I do not have a residential refer. The refer will greatly shorten that time.
The battery disconnect switch" near the battery disconnects the positive lead from the battery bank. Fully charged flooded cell lead acid batteries may last 6 months before needing recharge.
I wish you good luck and happy trails ahead!