Kakuryu got off to a winning start in the 15-day meet at Aichi Prefectural Gymnasium but sustained a foot injury during his first loss of the tournament against second-ranked maegashira Hokutofuji on Tuesday.
"Being prone to injury means he's losing power," Izutsu was quoted as saying by Kyodo news agency.
"If he can't win next time he steps on the dohyo, there will be no option to pull out midway. He would have to take the decision (to retire from the sport) as a man.
"His right foot got worse Tuesday evening and he had difficulty walking this morning. I feel bad (for the fans) that he has had many withdrawals recently. Though it is not his fault, it happened because he's not strong enough," Izutsu added.
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This was Kakuryu's third withdrawal from a tournament and he forfeited a bout in May with ankle pain.
The wrestler, however, remained optimistic about his future.
"I don't know what to say. I started on a good note so I don't know what went wrong," he said.
"I don't want to end with an injury this way, nor do I want to end as a loser. I hope to try and stay positive and overcome this injury."
(Reporting by Amlan Chakraborty in New Delhi; editing by Peter Rutherford)
