Inverter not cutting off before deep cycle danger level?
Inverted is set too low.

Battery will suffer.

Adjustment probably possible.

As it has got a shutdown system, worst case you can easily make your own monitor and tap into that point, probably. Worst worst cas is it's all done in softwrae with no hardware points in monitoring or shutdown that can be easily accessed. Impossible is nothing, but at some stage it's easier to replace the unit in some cases. Probably not here though.

Tell us more about the hardware integration level.
 Do you have a circuit diagram?
 Do you have a soldering iron? :-)