What must one do in the case of accumulated expiations, the number of which has been forgotten, after one swore not to commit a specific sin, and every time one commits it, one atones for their oath without renewing the oath?

A Muslim must desist from sin without making a vow. However, if one says, "Every time I do such and such, I owe an expiation," then one must fulfill their oath. The expiation is repeated with the repetition of the sin, because the word "كلما" (every time) implies repetition. Therefore, you are obligated to perform expiations equal to the number of times you committed the sin. Their estimation should be based on your best judgment, and increasing them as a precaution is more preferable.