What is acceptable voltage drop from PSU to controller?
Regardless of how the voltage is lowered, you aren't delivering the power to the heating elements that they are designed to deliver.  For a resistive heater, the power scales with the square of the voltage.

Delivering 11.4&nbsp;V to the heaters will result in the power being $11.4^2/12.0^2 = 0.9025$ or 90&nbsp;% of the intended power.

There are two things you could do to increase the power at the heaters.


Your voltage is starting out low, which you may be able to increase
at the power supply to 12.0&nbsp;V.
The voltage drop in the 1-meter cables can be reduced by using
shorter cables or larger cross-sectional area conductors.  13 gauge
is not a very heavy wire for low-voltage high-current DC.  I would
suggest 10 gauge, and would prefer 8 gauge.


The logic in the controller board should be fine as you are now.  Controller boards include regulators that being the nominal 12&nbsp;V down to the 5&nbsp;V or 3.3&nbsp;V required by the digital logic.  These will automatically adjust for changes in the 12&nbsp;V supply.

To actually answer your question, the permitted voltage drop is application dependent.  As a rule, though, I would suggest that the voltage on the pins of the controller should be 12&nbsp;&plusmn;&nbsp;5&nbsp;%, or from 12.6&nbsp;V to 11.4&nbsp;V.  The voltage you measured should be acceptable if it is the true minimum voltage.