I think you probably can. I don't think you will save money doing it.
The MSDS indicates it has a number of ingredients and I'm guessing that all of them need to be replenished to at least some extent after you somehow (safely) wash the accumulated lead out of the cloth.
If you don't want to buy another cloth, you can probably get by using a metal polish and paper towels. I don't know if that will be cheaper in the long run, but you might feel better about using something that's more obviously meant to be disposable.