The flight instructor of the Piper PA-34-200 stated that following an uneventful cross-country flight, his student configured the airplane for landing. On the final approach to the 2,500-foot-long by 50-foot-wide runway, the instructor advised the student that he was "low" and to "add some power." The student complied, and about the time the airplane reached the runway threshold, the student reduced the power as he flared the airplane. The airplane touched down "harder than normal and bounced." The flight instructor took control of the airplane and applied the brakes after it touched down a second time. The airplane bounced again, and when it touched down the third time, the flight instructor applied the brakes fully in an attempt to stop. The instructor considered aborting the landing, but did not believe that enough runway remained. The airplane departed the end of the runway, and went down an embankment into a ditch, resulting in substantial damage.