This is a good question.

I take it your concern is the the loss of the image. Assuming this correct, the statement can be taken two ways: (1) that Dr. Beeke thinks the image is completely lost in the fall or (2) that some aspect of the image is lost. The first option is, I believe, not intended. I would need further information to think Dr. Beeke takes such a radical (not to say, unbiblical) position. If memory serves me right (and it may not), the complete loss of the image was a view debated by Lutherans. However, I take Dr. Beeke to be taking the more or less common Reformed position that Adam lost the image of God in the sense of knowledge, righteousness, and holiness (things which are restored in salvation per Eph 4:24 and Col 3:10) and not in the sense of his humanity. In other words, the loss is ethical and not ontological. As Scott Oliphint would say, “Was Adam still Adam” after the fall?

The language one often finds in discussions of the image of God and the fall is that Adam lost the image narrowly considered, but kept the broader image. To use the language of Jonathan Edwards, Adam lost the moral image, but not the natural image.

Of course I am reading Dr. Beeke with a judgment of charity here. I could be wrong.

Jeff