I have a 1997 buick century. It started making a whining or hissing noise from the passenger side underneath?

I have a 1997 buick century. I bought it used but it drives really good and has a very quiet engine. It started to make some sort of whining or hissing noise from the passenger side underneath the vehicle where the muffler is located. It will let you drive for about 15 to 30 or so minutes then it stalls. Have to let sit for a minute then starts back up to stall once more. This car has been very great since it only is being used to take my kids to school and home. Any help from anyone will be well appreciated. I have had the oil change in and also had a tune up. No oil leaks and it does not run hot. Thanks, Also had the fuel filter changed also. Gas mileage is great so it does not burn gas at all.