Having this issue on multiple boards and multiple connect-board ‘board-relation’ columns. Not sure when it became a problem.
Per https://api.developer.monday.com/docs/connect#reading-the-connect-boards-column - the API should return the data.
Hello @bmack!
We are going to need you to please send this information to appsupport@monday.com so we can take a closer look into it, look into the logs and give this issue some following 
Have either of you gotten a resolution on this? I have recently experienced the same issue.
I submitted a ticket in with Monday.com support shortly after posting. Have some dialog back and forth but no fix at this time.
fyi…