Executives from Mecca Bingo Ltd - which has traded under the name since 1884 - were unable to agree a solution with community leaders at a meeting yesterday.
Sections of the community have been outraged since the renaming in November of the bingo hall, previously called Top Rank. They said it was an insult to Islam for the name of their holiest city to be associated with gambling, and on Christmas Day, bricks were thrown through windows at the hall, causing pounds 3,000 of damage.
Councillor Hazel Simmons, chairwoman of equal opportunities at Luton Borough Council said: "We are aware of a groundswell of public opinion and I personally believe this to be insensitive in what is now a truly multicultural society."
But Mecca Bingo said the name change was not insensitive and was part of a policy of bringing their nationwide chain of bingo halls under one name.
Sergeant Peter Shepherd, community liaison officer with Luton police, said: "It was unrealistic to expect that anything definite could be resolved at the meeting, but at least it was constructive to have the dialogue."