Have your batteries load-tested, I think you'll find at least one of them is faulty if they are the OEM batteries.
Another aspect;
Do you have a setting in your inverter for a low battery alarm? If this is set above 11V, then while the battery bank is being drawn-on the alarm will usually sound. While the inverter is drawing on the batteries they are depleting @ 10X the AC amperes being produced.
So if your appliance is drawing 10A AC, the batteries are losing 100A DC per hour.
You might find this interesting reading:
The 12volt Side of Life (Part 1)
__________________
2000 Winnebago Ultimate Freedom USQ40JD, ISC 8.3 Cummins 350, Spartan MM Chassis. USA 1SG, retired;PPA,Good Sam Life member,FMCA.
"We the people are the rightful masters of both the Congress and the Courts - not to overthrow the Constitution but to overthrow men who pervert the Constitution." Abraham Lincoln