Can I make the mechanic fix it free of charge?

I was driving on Thursday of last week, when my car randomly shut off (exactly as it does when it runs out of gas-- lurches forward and sputters a little bit, then the engine shuts off-- still have batter power, though.). I took it to the shop to have it fixed, and the mechanic said it was the fuel pump. So, I paid $420 to have it replaced. I pick it up this morning, and after driving 5 miles, the car died again-- exactly as it had done before. The tow truck came and got it and brought it back to the shop. I just called them, and they said it might be a regulator, but they're not sure; they're doing more research and are going to call back. If they try to charge me for another repair... can I tell them to fix it for free? What's legal here?