What has been the maximum number of failed landing attempts for any commercial flight yet? Top DGCA officials say they do not recall any other instance of this kind where a plane tried to land unsuccessfully six times and then finally touched down in the seventh attempt — whether in India or abroad. (Source)


A better written report of the incident.

Coming to the question, what has been the maximum number of failed landing attempts for any fully loaded commercial airliner?
As far as I know, nobody actually maintains a register of go around. A go around is not a failure, nor a fault.

However each missed approach reduces the fuel quantity which may become insufficient. The crew will not continue to try to land at the same airport if the likelihood of better conditions at the alternate airport are high.