I've had the same problem but I have fixed it. The replacement belt is not a 5/8 inch x 38 inches. It should be a .59 inch x 37.75 inches. I have been searching for a different belt and it is available at VBeltSupply.com and the part number is V-408010 and a description of "Sears / Roper / AYP Impeller Drive Belt Replacement". The SKU is OEM12&205.
You will notice that the part number is very close to what is often quoted as the replacement belt.