You might check the battery connections. Clean them real good and ensure they are good and tight. Sounds like a complete loss of power. Do the headlights work when it goes off? I have 2 '97 Lesabres and have experienced a dying issue with one of them, but I do not entirely loose the electrical, the radio does not reset. My problem turned out to be the MAF sensor. Sounds like you have a different issue though if you are completely loosing power. I would check all of the ground wires to ensure they are good and clean plus making good contact. Right after it happens, will the starter even turn over, or is it completely dead?