2006 not starting sometimes, also starter 'runs on' after ignition
 

My wife's Lacrosse has been acting up lately, and our oil change guy said he thought the starter had sounded week for quite a while. So I replaced the starter with a new, OEM AC Delco starter. The starter has given her quicker and stronger starts, but for some reason, the car won't start at weird times. She now has told me that although it will start fine a lot of the time, it has failed to start (correctly) after fueling up at the gas station(??) 3 times now. She said last night that's the only place this has happened in the last week. I've read that could be caused by vapor lock, but she usually gets gas right after she leaves the house, so it's not actually hot enough for a vapor lock. Also, it's February and not even in the 60's when it's happened.

Also, she tells me that it's sometimes what sounds as if the starter solenoid is stuck, in that she says it keeps cranking after the car is running, then she shuts it off for fear of messing something up, then starts it up again and puts it in gear and floors it to get out of the gas station.

If the starter is new (not remanufactured), and this is still going on, what could the problem be? I was watching some youtube videos on a problem my adult daughters car is having, and ran across a few that mentioned that the MAF sensor may need cleaned? Seems like a long way away from the problem. What's your opinion on this? Thanks, Lee