Sometimes its caused by a gear mismatch:
Open the ai.ini and engine.ini inside the 'data' folder (if the car has a data.acd, unpack it with content manager first)
Make sure the Gears UP value in the ai.ini:
[GEARS]
UP=7900 (wrong value)
DOWN=4600
SLIP_THRESHOLD=0.95
GAS_CUTOFF_TIME=0.130
has a lower value, than engine.ini limiter
[ENGINE_DATA]
ALTITUDE_SENSITIVITY=0.1 ; sensitivity to altitude
INERTIA=0.120 ; engine inertia
LIMITER=7500 ; engine rev limiter. 0 no limiter
MINIMUM=1500 ; engine idle rpm
LIMITER_HZ=50
In this example the RPM needed to shift up is higher than what the engine limiter allows, so you would change the ai.ini value to something like 7200
It doesn´t work every single time, but it might be the case for the cars you´re trying to run.