Randomly shuts off

I bought this car for one of my kids. It has 130,000 on the clock which I understand is not much for these ES300's. I have taken it to two mechanics that could not figure out the problem. I have performed multiple searches here and online for some help, but to no avail. The car has the infamous P1300 (code igniter fault) and the car randomly shuts off regardless of speed, temperature, load, or distance. It will be driving beautifully and just shut off randomly. I pull the car to the side of the road and after some cranking it fires right back up again. I have had the car to two mechanics and they cannot figure it out. Sometimes it runs for five minutes and shuts off and sometimes two minutes and shuts off, completely random times and speeds. I know the mechanics tried a replacement ECU, checked and changed coil packs, ignition module, checked battery terminals, and cleaned the idle air control valve, but the engine continues to shut off randomly. I am hoping that one of you can perhaps provide a little insight as to my next course of action with this thing as its got some good years left in it. Thank you in advance for your reply as they are greatly appreciated. Cheers, Jay