Flight Instructor in a C172 reported the flaps would not retract on initial climb and return to departure airport.

Narrative

Upon conducting a touch and go and setting flaps 0; the electronic flap system did not raise flaps from full (30 degrees) to up (0 degrees). The aircraft became airborne and climbed to an altitude of 500 ft AGL before leveling out. PIC immediately began monitoring control feel and airspeed to prevent a stall or other loss of control. The aircraft had difficulty climbing further; and PIC decision was to return to the airport (ZZZ) to land while in the departure leg of the traffic pattern. An announcement was made on CTAF and other aircraft were helpful with departing the traffic pattern so our aircraft could turn downwind and land uninhibited. Airspeed and altitude were both able to be maintained while in the traffic pattern; but returning to our home airport (ZZZ1) was deemed to be a risk PIC was not willing to take. While airborne the flap control was cycled as well its circuit breaker. A full stop landing was performed and the aircraft was secured on the ramp with tie downs. No injuries or damage to the aircraft or airport occurred. An A&P inspected the aircraft and found a faulty relay switch behind the firewall connected to the flap control. A pre-flight inspection would not have identified this issue.