It's inconceivable that air traffic controllers could have lost track of any of the hijacked aircraft, just because they turned off their transponders. It should still have been possible to track them through primary radar
Air Traffic Controllers make use of two different radar systems.
Secondary radar uses transponder information to display details about a plane like its identity and altitude, so is the most important.
In the absence of a transponder signal, controllers must pick out an unidentified blip on the screen from all the other aircraft they're dealing with, not such an easy task. And it's further complicated because some areas don't have primary radar, meaning a plane passing through them with no transponder signal simply disappear. The FAA Aeronautical Information Manual confirms this:
At some locations within the ATC en route environment, secondary-radar-only (no primary radar) gap filler radar systems are used to give lower altitude radar coverage between two larger radar systems, each of which provides both primary and secondary radar coverage. In those geographical areas served by secondary-radar only, aircraft without transponders cannot be provided with radar service. Additionally, transponder equipped aircraft cannot be provided with radar advisories concerning primary targets and weather.
FAA Aeronautical Information Manual
February 19, 2004