New York City showed resilience when it rebuilt the World Trade Center after the Sept. 11, 2001, terrorist attacks, but the project was also supposed to generate profits that could go toward bridges, tunnels and airports.

Now, nearly five years after the office tower at One World Trade Center opened, the World Trade Center complex as a whole is still losing money. That is largely because costs related to security efforts to prevent any future attacks are making it hard to break even.

The...