C172 flight instructor with student reported a taxiway excursion due to brake failure.

Narrative

While taxiing to Runway X on delta; student pilot was taxiing slower than a brisk walk; student pilot went to make the right turn where the taxiway curves right to hold short on Runway X on delta. Aircraft did not turn; student pilot pulled throttle idle and applied brakes; and the aircraft did not stop. As the aircraft got closer to the edge of the taxiway; instructor pilot also pressed on the brakes and pulled back on yoke for aerodynamic braking; still the aircraft did not stop. Was not able to maintain directional control to stay on taxiway. Aircraft went straight off of taxiway; instructor pilot managed to point aircraft slightly to left and to avoid going into a deep ditch. The aircraft came to a stop in a tree. Both student pilot and instructor pilot were uninjured.Cause: The aircraft had previously been written up for maintenance by another instructor the day of the event. The instructor reported that the right brake pressure was inconsistent and they had lost brake pressure on more than one occasion. Maintenance signed the aircraft off for return to service. Same happened to us as the brakes worked up until the event.Suggestions: Instructor pilot reviewed the maintenance write-up regarding the brake issue prior to starting the airplane. After starting and just after commencing taxiing; we checked the brakes for correct operation while taxiing out. Since the brakes were set and held during the engine run up and were still working; it would be hard to assume they were not operating correctly. At that point; there is not much else one could do to further ensure the brakes operational condition.