Transmission problem
2000 BMW 328 6 cyl Two Wheel Drive Automatic 130000 miles
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I am going 60mph and when accelerating at that speed, the engine shifts down into third gear and orange warning light comes on. Light goes off when I stop the car and turn the engine off for 15 seconds. But continues to do the same the next time I am going 60 and accelerate.

The first thing to do is to get the car scanned with the BMW proprietary software either at the dealer or at an independent and report back to us with the findings. This is possibly a software issue.