Very ambiguous section. The language says, "No further retests shall be given until the welder has submitted proof of subsequent welder training that is acceptable to the company." What is acceptable to your company? Practice? 1 joint or 10 joints? Just a review with the radiographer? Do you require documentation?

You'll see this addressed where the welder was sent back to their union hall for documented training, you'll see just a verbal consultation by a CWI only (lacking in the "submitted proof" area in my opinion) and you'll see where the welder was not allowed to retest at all - sent packing.

API 1104, 21st Section 6.7

If, in the mutual opinion of the company and the contractor's representatives, a welder fails to pass the qualification
test because of unavoidable conditions or conditions beyond the welder's control, the welder may be given a second
opportunity to qualify. No further retests shall be given until the welder has submitted proof of subsequent welder
training that is acceptable to the company

Not really ambiguous. Pretty clear.

If the company and contractor agree, the welder can be allowed a retest if it is shown the failure was not due to the welder's ability but due to conditions. Otherwise (or After that), they must show documented training.