A critical hearing regarding the proposed nine-story hotel abutting the Merchant’s House Museum is scheduled for September 4, the museum just announced in an e-mail. Following the hearing, the Landmarks Preservation Commission will either give the green light for the controversial hotel, or send the developer back to the drawing board. Supporters of the museum consider the proposal dangerous because construction could undermine the structure of the 180-year-old building, as well as its aesthetic. Still, there’s no guarantee the hearing will take place on the scheduled date — it’s been postponed four times already. “Hopefully we don’t have a fifth postponement,” said Emily Wright, a museum spokeswoman. “We’re still of course very concerned, the potential for damage is very serious.”