2004 VW Jetta

If the engine is cutting out while driving, you should be getting a "Check engine" light.

If so, have your computer scanned for codes.

If not, then I would thing you may have a vacuum leak or possibly a faulty/leaking fuel pressure regulator. There's also a possibility of a faulty/dirty mass air flow sensor. These are known to cause a stumble at low engine speeds with often cut-outs.

If you're interested in doing this work yourself, let me know and I'll walk you through it.