Saturn Vue engine quits while sitting still

Our 2003 Saturn Vue has recently begun quitting while sitting still. There is no problem driving it but once we come to a stop it will cut off - occasionally, not all the time. We have had it in the shop and thoroughly gone over. A new battery was put in 5 days ago b/c it would not start (this is ultimately when the problem began). The oil light and battery light stay on after it dies and it smelled of oil inside the car the last two days. The times the car has shut off has only been about 5-10 minutes after beginning to drive it. Would love some input!

Is the check engine light on?

When it dies at idle, how does it die? Relatively sudden cut off? Surge and fall/surge and fall …die?

One of the first suspects for stalling at idle is the idle air control (IAC) valve. (more prone to lead to sudden cut-off).

Another kind of suspect is a vacuum leak. (More prone to surge & fall & die in fits and starts).

All of the basic dash warning lights (including battery and oil) come on when the ignition is engaged without the engine running.

On first guess I’d say that the battery and oil smell issues are separate - though you should have it evaluated for oil leaks. That won’t make it stall at idle though. The only thing I could think of related to the battery is that on many (all?) cars these days the computer has to “relearn” basic air/fuel mixture settings when the battery is disconnected. Yours could still be learning? (But I think that is a stretch).

The check engine light does not come on and the car just cuts off, no fits and starts. The mechanic also mentioned the computer re-learning settings when they couldn’t find anything. They kept it two days but it did not shut off on them and drove fine all day today until later in the evening when it shut off twice, thankfully after I got home. Also, it doesn’t start right back up, I have to wait a minute or two before it will completely turnover and start. Thanks