Even at the risk of economic loss, he . . . . . . . refused to take the beaten track.

The correct answer is E. steadfastly.

The other options are incorrect because they do not convey the same meaning of determination and persistence.

• Repeatedly means “again and again.”
• Often means “many times.”
• Regularly means “at regular intervals.”
• Continuously means “without interruption.”

In the context of the sentence, the man is refusing to take the beaten track, even though it means risking economic loss. This suggests that he is determined and persistent in his beliefs. The word “steadfastly” best conveys this meaning.