FOnlineAsyncTaskManager::Run waits for the WorkEvent to trigger before it will tick. However, this event only gets triggered if there are new Available Tasks.
Therefore, even though there may be pending Parallel Tasks, they may never get updated.
Create an FOnlineAsyncTask, and add it to the FOnlineAsyncTaskManager.
Notice, that when there are no Active Tasks, it doesn't get ticked.
There's no existing public thread on this issue, so head over to Questions & Answers just mention UE-54420 in the post.