Act as a sounding board
Sounding bored.... uhh... Sounding Board!
For example: When engaged in a workshop meeting, or perhaps any general meeting, acting like a sounding board, by either repeating what was said another way, or adding context will almost always help not just the person telling the story, but also the other stakeholders in that meeting with you.
I've have often attended sessions where a deeply important issue is being raised, but you can sense the frustration in the voice of the speaker and sense also that no-one around the room is quite there with what the issue is actually about.
As BAs one of our primary roles is to understand the business, the stakeholder, the general feeling and consensus etc.
Take the initiative, to try replay the story, break-it-down if needed and see if you can relate it back to why it was raised and whether its relevant for the discussion at hand.
Sometimes something may need to be discussed offline, and other times a discovery of a point is so important, that it will warrant its own separate discussion.