Shredding belts on a 2000 Taurus

I have replaced the serpentine belt on this 2000 Taurus (101552 miles, 3 liter V6) 3 times and the belt works for 250 - 300 miles and the edges shred again and finally breaks.
A Ford dealer also replaced the belt twice and again the fraying belt and breaking.
A/C on of off makes no difference
Replaced idler and tensioner
Replace alternator
Checked all pulleys for dings etc.
Checked pully alignment
Using a good year Gatorback belt

The customer is back with the edges of the belt beginning to fray anter 150 miles.

Can you help please - we are at the end of our resources.