The more watts your device uses the quicker it will drain the battery. 1000 watts at 12.7 volts uses 78 amps, but once your battery goes down to 11.7 volts those 1000 watts will use 85 amps. The lower voltage battery will put out more amps at lower voltage to maintain the 1000 watts As the battery voltage goes even lower it will use even more amps.
A good youtube video to watch is "lithium battery test versus gel" , on this test they test 3 batteries a 100ah lithium, a 100ah lead acid and also a 220ah lead acid, they use a 2600 watt load(heater) and run it until the the heater shutsoff from low voltage. The lithium voltage drop to 11.7 volts and was putting out 285 amps(lasted 21 minutes), the 100 ah lead acid voltage drop to 10.2 volts and was putting out 325 amps(lasted 6 minutes), the 220 ah lead acid battery drop to 11 volts and was putting out 305 amps(lasted 13 minutes). The lower the voltage the more amps it used, you need a large lead acid battery bank to keep the voltage high.
When you turn off your heater, your battery should be reading at least 12 volts, if it reads less then that, your draining it too much. If the battery gets down to 11.5 volts or lower without load and you don't recharge right away it won't last long. I destroyed my agm by taking it below 11 volts about 3 times. The sweetspot is not to take the battery below 12.1 volts(no load), it will last years.
If you can't use the mr.heater, add more insulation. The more insulation, the less you have to run your electric heater, you can run it on the lowest setting for a few minutes every once in a while.