Car keeps turning off. No check engine light.

Hi, This problem should be looked at by a qualified driveability technician that would know where to start. However take a look at the fuel pressure regulator. The SLX had an issue with the internal diaphragm tearing. This would cause fuel to stream directly from the regulator into the intake manifold. This caused the car to stall and usually did not have a check engine light. Remove the vacuum line from the regulator and see if there is fuel present. If there is fuel, the regulator needs to be replaced. If there is no fuel, take the vehicle to a qualified repair shop