99Merc

I dont know exactly how to explain this, but Ill do my best so please bear with me. Occasionally (as in maybe once or twice a day) when my girlfriend is driving her car (99 Grand Marquis) it will lose power and you wont be able to accelerate. Usually this is going up a hill or on a bumpy road, but I dont think its always like that. Ive had it happen to me once while with her and it felt like it was starved for fuel. If you barely kept your foot on the gas you could keep your speed up kinda close to where you were before. I was going about 60 and I could maintain 50ish mph until I hit a hill. When you mash the gas nothing was happening. Didnt sound like the trans was slipping or anything. I pulled over and it was running really rough like it was about to die...but the weird part is once you turn the car off and let it sit for about 60 seconds, you can restart it and go again till it happens again. She was in a fender bender about a month ago and the red button near the gas door (in the trunk safety feature) needed to be pushed in. Is it possible that the sensor in that box is throwing a faulty signal and restricting gas flow even though the button has been reset? This just started becoming an issue after her accident. Thanks in advance for any help you all can give me, Im at a loss...