Have you taken the battery to a "battery shop" or "auto parts store" and had it load tested? That's the first step, I think. A battery can be "charged to 12+ volts and show that on a multimeter, but can be unable to discharge that voltage into the circuit when required because of sulfur buildup on the plates.
Here's a "pretty good quick explanation" I found:
A Lead Acid Battery is made up of plates of lead in a case filled with an electrolyte (dilute sulphuric acid). When the battery discharges, some of the lead from the plates combines with the electrolyte to make lead sulfate (PbSO4) which builds up on the surface of the plates as crystals (as electrons leave the battery as electricity). This is called sulfation.
When the battery is next charged this process is reversed with the lead sulfate crystals breaking down - returning the lead to the plates and restoring the electrolyte to its original composition. BUT, each time a battery goes through this discharge/charge cycle some of the lead sulfate crystals remain and over time harden, thicken, and grow over the surface of the lead plates. This is a particular problem when batteries are left discharged for long periods of time and when they are deeply discharged.
Lead sulfate on the plates of a battery acts like an insulator reducing the plate area in contact with electrolyte. Over time this build up of lead sulfate crystals will result in a battery which cannot hold much charge - i.e. effectively a dead battery which needs to be replaced.
It came from this link:
http://www.reuk.co.uk/Battery-Desulfation.htm
I wouldn't recommend trying to build a "home made desulfation device" rather have the battery tested and if it won't support a load, buy a new one. The way RV converters "protect" against sulfation is to increase the battery charging voltage to 13.6 VDC for a period of time at the beginning of the charge circuit. This happens at the beginning of every charge cycle. But, if your RV is plugged in "continuously" and the battery is never discharged, that "desulfation" isn't done as frequently as needed. That would put your battery (over a period of months/years) in a "constant state of partial charge/discharge without desulfation and may be why your battery won't charge/support a load.
If you put a multimeter on the battery (with the shore power disconnected) and try to open the slide, you'll probably see the voltage across the battery drop to 6 or 7 volts if the battery is unable to hold a load. A load check at an auto parts store would confirm the problem.
Linear Mode
