Bewley's chief executive John Cahill said this was due to a "grossly excessive rent" of €1.5m a year that is paid to landlord Ickendel Ltd, a company controlled by property developer Johnny Ronan.
Ickendel's loans have been transferred to NAMA.
A legal dispute has broken out between the parties regarding a five-year rent review that was due on January 1, 2012.
The dispute was before the High Court in November and is listed to be heard again on March 21.
The Grafton Street cafe, opened in 1927, is one of Europe's most renowned coffee and tea emporiums.
It closed in November 2004 for a brief period and reopened in May 2005, after refurbishment and restoration.
Bewley's lease on the Grafton Street cafe includes an upward-only rent review clause. Its rent in Grafton Street rose in 2007 to €1.46m from €750,000 in 2002.
This was just before the property bubble burst and Mr Cahill said the current rent is no longer sustainable.
"You are looking at a 50-55pc reduction in market rents since the peak in 2007 -- that's well documented," he said.
"We are loosing about €700,000 a year on the property and you can attribute all of that to the last rent review."
Bewley's achieved group sales of €85.4m in 2011, up 10pc on the previous year.