We had a situation where the Flesh Rippers made an enemy unit retreat, the the Rippers used Pursue to move to the enemy's original hex, and attacked.

The Rippers failed to eliminate the enemy unit, so the other player wanted to know if he could Counter Attack, can he?

In other words, can a unit that has retreated counter attack an enemy that uses Pursue on them?

Thanks!

Yes. Let's look at the wording: Pursue allows you to perform an additional Attack. Counter are triggered by attacks. So, if the attacked unit survives the second attack and is not forced to retreat, it may perform the counter.

Thanks, that's what we thought. So that basically makes it where it may not always be wise to use Pursuit, especially if you make the enemy retreat off of a hex that you want to move onto and keep, such as a hex with a VP marker on it, right?

Yes, exactly, whether using Pursue or not is just part of the general strategy: sometimes it's helpful, sometimes not.