The tricolour was hoisted last month but keeps getting torn by the wind and is being replaced for a fourth time.
It was launched with media fanfare but now officials say national pride is being dented and money wasted.
Pakistanis are likely to be amused - the aim was for the flag to be seen from deep inside their territory.
Indian press reports at the time said the 106m (350ft)-tall flag at the Wagah crossing would be visible from Lahore, 20km (12.5 miles) away.
Instead, officials have had to spend more money on replacements because by law a damaged flag cannot be flown.
Suresh Mahajan, the chairman of the Amritsar Improvement Trust, which is responsible for maintaining the flag, said that the situation amounted to a "crime".
"The national flag is our pride and I request the government to call an inquiry over the issue and those responsible should be punished," he told BBC Hindi.