Epernay opened inside The Electric Press on Great George Street in 2005, billed as the city's first dedicated champagne bar.
It also had a cocktail menu, but re-launched under new ownership in early 2017 and returned its focus to fizz.
The bar is believed to have closed in August, with a sign in the window saying it had shut 'until further notice' - but it has not re-opened.
Its website appears to have been taken offline and its social media accounts have not been updated since August.
Twitter user Daniel Jones complained he had not been contacted by the business about an advance booking he had made before the closure in August.
"My wife and I had a champagne tasting session booked in for today. It was booked a few months ago. We arranged for a babysitter and arrived to see this. It would have been courteous of you to let us know, so we didn't waste money and spoil our plans."
After the re-launch last year, the management began table service, got ride of the cocktail list and introduced high-end champagne including a 1990 vintage Dom Perignon for Â£500 a bottle.