The much-delayed hearing regarding the proposed nine-story hotel next door to the Merchant’s House Museum is now set for Sept. 11. This is the fifth time the hearing has been postponed: Previously, it was scheduled for Sept. 4 after the developer of the hotel requested more time from the Landmarks Preservation Commission to prepare a presentation that will likely seek to allay the many concerns of museum supporters. Critics have said the hotel could threaten the foundation of the museum, and that its size would diminish the historic qualities of the 180-year-old building.