If you have a lead acid battery, it might be toast. Lead acid batteries shouldn't be discharged beyond 50%. Draining them further than that damages them and they don't seem to recover well. For example if you have 100 AH battery it might be only capable of 80AH, which would mean that you've only got 40AH of useable power.
I would make sure that the converter is working properly. Find the breaker in the AC panel that feeds the converter and make sure it's flipped on. Just to be safe, flip the converter breaker "off" and then flip it "on" again. Once you're 100% certain that the breaker is "on", measure the voltage across the battery and see what you get. Charging voltage for a 12V battery can range from 13.8V to 14.4V during bulk charging, with a float voltage around 13.5V to 13.8V to maintain a full charge. If you don't read the higher voltages I would turn "off" your converter and then disconnect the battery. Once disconnected make sure the leads aren't shorted out or touching the frame. Then flip the converter breaker "on" again and read the voltage across the now disconnected battery leads. You should read at least 13 to 14 volts. If you don't read that, your converter has some sort of an issue. It could be burned out or have a loose wire.
Lastly, if it turns our you battery is toast I'd replace it with a Lithium battery. Your converter may be lithium capable if not it will still charge a lithium battery, just not to 100%. It may only charge it to 80%, but unlike lead acid cells, you can almost fully discharge lithium batteries without damaging it. I'd just buy a lithium battery with a BMS that has low temperature charge protection.
I hope this helps.
Bob