A complete stop the engine shuts off

Will it hold an idle? Sounds as if the base idle is to low. Also, run a scan for any codes, not all codes will set a check light. Check for vacuum leaks and do a fuel pressure test as well. Start here.

Can you give me the code? O2 sensors can give bad reading due to vacuum leaks, up stream exhaust leaks, high or low fuel pressure, faulty injectors, and general tune problems. A live data read will show if the O2 sensor is just out of range or has failed completely. This would be worth checking as well.

Secondary air injection system code.

Potential causes for a P0491 may include: Faulty exhaust manifold check valve A fuse or relay for the secondary air injection pump may be faulty A faulty air pump Leaking vacuum hose A bad vacuum control switch A dislodged a vacuum line A leak in the hoses/piping between the secondary air injection pump and the Combi or secondary air injection A sensor for the secondary air pressure may be faulty The combi valve itself is faulty The secondary air injection port in the cylinder head may be plugged with carbon The secondary air injection ports in the cylinder head may by clogged