I also think it's the problem with 12V being low. A car battery that's not being charged will definitely be low, as it's barely 12 volts in fully charged state.
Why don't you believe it when it tells you the input IS low?
What input voltage does it show on the Pulsar when this happens? Have you measured with a voltmeter?
The reason it doesn't happen with 35GFX is because ithe 35 probably has voltage multiplier circuit built in and isn't so sensitive about input voltage.