This imbalance often makes the more active partner feel guilty and/or the less active feel jealous, insecure, etc. As a result, the more active may offer the less an opportunity to close part or all of the relationship.
I am deliberately formatting the following statement unpleasantly, to make sure it permeates:
The decision to close an open relationship
(even when "closing" relates to a single person rather to the relationship as a whole)
should ONLY EVER be made
by BOTH partners JOINTLY.
If your partner comes to you and says, "I will stop seeing X if you want me to," don't take the [well-intentioned] bait. Open partnerships are partnerships first and open second. One person calling the dating shots for the other breeds the most corrosive sort of resentment.
There are a million ways to approach the inherent imbalances of dating outside your primary relationship, but all of them start with talking to your partner, and end with making decisions together.