1999 Sportage problem

My '99 Sportage (62Kmis.) starts fine, and idles fine. When I step on the accelerator, the engine starts to cut out. It won't die, but will return to a normal idle when you let off the accelerator. I tried cleaning the idle air controller. The timing belt was changed at 58K, along with the coil pack, plugs and wires. The check engine light is off. Do you think this could be the fuel pump? Please help!

Update... I disconnected the battery for a couple minutes, and now everything seems to be back in working order.

It's not the fuel pump and the problem will come back.

There is corrosion and/or loose connections to the mass airflow sensor. The MAF is the round plastic piece between the air filter and the rubber flex pipe. It has an electrical connector on the backside. That connector is the culprit. Remove the connector and clean and recrimp all the contacts.

That should fix the cold stumble. But it will be a temporary solution. The corrosion will eventually return. A permanent fix is to cut off the connector and solder the wiring directly to the tabs on the MAF.