Why did Lincoln and Shepard continue to chase the Regulators?

Lincoln and Shepard continued to chase the Regulators because they were determined to bring an end to the lawlessness and violence that the group represented. Their pursuit was not only about enforcing the law but also about restoring order and protecting the community from the chaos caused by the Regulators' actions. Additionally, they sought to uphold justice and demonstrate that such unruly behavior would not be tolerated.