There is a limited number of pass holder seats on the Eurostar and on popular departures and during high season those sell out weeks, and sometimes months in advance.

The best place to see the availability of passholder seats on the Eurostar is 

https://www.b-europe.com/EN/Booking/Pass#TravelWish

Press "later trains" and eventually you will find the next available connection. 

If you have a mobile pass you need to generate a Pass Cover Number in order to make the reservation at b-europe. You do that here in the PCN generator:

https://community.eurail.com/news-and-announcements-39/pass-cover-number-generator-is-live-5653

Just made this trip yesterday, mid-aftern, but to BRU and the car I sat in was about 25% empty.

As I was bored checked its site and ´low fare finder´ : IF you cannot find seats for that group on that day-move to mo-thu, weekends, from FR on are far busier and cost more. But late sept showed already quite a few days with ultra-low normal fares-(39€/single) fo to go BRU and Rotterdam.

If that is the only trip to make that day on pass-consider this afetr checking