There should be a limit on the amount of times you can retake a test to become a fire fighter because it is a very serious job. It is also very demanding. You must be in great physical condition and you must be willing to get into dangerous situations. If you can't pass the test then you don't need to be a fire fighter and you need to find a different job that suits you the best.
If the FDNY doesn't regulate the number of time applicants can retake tests, they would be cheating those who've taken them successfully and proved their worth. This is just another way for making cheating and bribery possible. I definitely think test-taking should be limited to a reasonable and appropriate degree.
The FDNY should set limits on the number of times an applicant can retake a test. The more an applicant takes the test, the more familiar they become and it becomes less of a test of their overall knowledge/skill set. It's important that the FDNY (and other fire departments, too) receive the cream-of-the-crop applicants, and this means setting testing limits.
In sectors where public safety are concerned, every precaution should be taken to ensure that the sectors' employees are thoroughly qualified. An unlimited number of attempts at taking FDNY tests does not ensure quality control and defeats the purpose of testing in the first place. Some applicants may not test well, but still be qualified, however, limits are a necessity.