You should be submitting all welder qual records to the customer, usually through their engineer, for approval.  As long as you are keeping good records there should not be a problem. 

But, a customer can always request that all welders be requalified and even that a representative of their choice, or an independent lab, witness and/or perform the testing. 

Pretty sure that is as applicable with ASME as it is D1.1. 

He Is In Control, Have a Great Day,  Brent