I am frustrated! I have a 96' Bonneville and the engine keeps cutting out when I am driving down the road. In higher RMPs it seems to run fine. In lower RMPs is runs O.K. as long as you don't push the gas too hard. When you are running low RMPs and push the gas to accelerate more than 1mph/sec the motor will kill and then backfire. If I am going 55 down the highway and the car is in overdrive and i step on it the motor will die. It can not downshift because the motor doesn't run up the RPMs to drop it a gear. So I have to manually down shift, accelerate, and then put it in OD. I have replaced the sparkplugs, the wires, cleaned the air/gas sensor, and even took out the honeycomb in my convertor to try to fix it. Any ideas? There are no codes and the check engine light is not on!

Air/gas sensor? You mean the oxygen sensor on the exhaust? Is this a naturally aspirated engine (non-supercharged)? My thoughts are MAF sensor or TPS or PCM. I bet there are some codes in there, you just need a scan done.

MAF,TPS,PCM?? Sorry I am noob...

Mass Air Flow sensor, Throttle Position Sensor, Powertrain Control Module

They are all critical to proper operation.

you may have a stuck valve that would cause it to backfire... As for it dying I'm not sure.