In the case of a power source with plenty of power delivery available, the implication is that regulation is at fault. If you were to look at a desktop PC with a good high power 12V rail you would find that a battery would fail for this too. The battery is capable of more delivery current than is even a 1000W high end power supply, but the power supply is far better behaved.
Can you add a buck/boost regulator? Or at least some sort of regulation? Without this I suspect it will fail.
As a side note, never ever connect any computer directly to the battery of an automobile. Spikes and regulation issues could actually damage computer equipment. There must be protection against the issues of inductive loads (such as starter motor and distributor coils or alternator), and I suspect this is even worse than attaching a computer to a house wall power connector without a surge protector.