I would normally have suspected that the ADC unit has input diodes intended to "clamp" its inputs' potentials, to prevent them from falling far outside the ADC's own power supplies. If the ADC's supply is 0V, then you can expect those diodes to seriously mess up the signal, since they will effectively clamp that signal to near zero. While this is a possibility, you mentioned the problem occurs sporadically even when the ADC has power, which would seem to point to another different issue.
If the ADC inputs are very high impedance, and the measured-signal's source impedance is less than 100Ω or so, then the solution could be simple as this:

simulate this circuit – Schematic created using CircuitLab
R1 here simply limits current drawn by the ADC's input protection diodes, preventing them from short-circuiting that signal to near ground potential.
Alternatively, it's not hard to use an op-amp to provide some degree of additional isolation between source signal and ADC:

simulate this circuit
The input impedance of the op-amp is so high that even 100kΩ (R1) of additional input resistance will only introduce a few millivolts of error. You can reduce that to near-zero by using a FET input op-amp. The op-amp can have input protection diodes too, but R1 will prevent them from heavily loading the source signal in the absence of a power supply to the op-amp or ADC.
R2 prevents an unpowered ADC (whose inputs are clamped near 0V) from short-circuiting the op-amp's own output to ground, but by placing R2 inside the feedback loop, it will not affect the "voltage follower" action when the ADC is powered.
Of course, this is an automotive application, and this simple approach does not address the problem of a dirty 24V supply, spiking to perhaps 50V or more, which could easily destroy the op-amp. The supply doesn't necessarily need to be 24V; if you only need up to +5V output, then a +7V supply would be fine too. Whatever supply you use for the op-amp, it will need to be cleaner than a typical automotive +12V or +24V supply.
The other caveat to this solution is that no op-amp with a 0V "negative" supply potential will be able to output 0V. Using the LM324, for instance, a typical lower limit might be +40mV or so. If the source signal is expected to reach 0V, and you require the op-amp to follow it all the way down to 0V, then you'll have to provide the op-amp with a negative supply too, perhaps -1V.
That's as much as I can say without knowing a lot more about the ADC, the source signal, the measurement accuracy you require, and the signal/sample frequency.