Loss of power on low fuel???

So this has me puzzled, I don't know where to go so I thought id share and see if anyone knows what is wrong and how i can fix it. My 2001 gti vr6 runs fine on a full tank of gas all the way until about an 1/8th of tank when all of a sudden there is a loss of power. It only happends at a unaccelerated speed. and usually between 40-80 mph. The car just stop getting power and decelerates, the only way to get it to snap out of it is to downshift and have high revs then it goes back to normal, and like i stated earlier only happens when i have low fuel. I was wondering if anyone can help diagnose this and potentially help me fix this problem.

If it helps at all I have a 2001 Gti vr6 with 115,000 miles on have changed serpentine belt, temp gauge, alternator, batteries, and plug wires and only put 91 fuel it it......when I was gone for almost a year I had a family member borrow my car and the said they put 87 fuel in it hope this helps with the answer.............

i wish i could help. but ALL i can say is dont get so low on gas