DA42 flight instructor with student reported engine issues during takeoff resulting in an immediate return to the airport. Reporter stated a second attempt to takeoff resulted in a rejected takeoff due to right engine not producing enough power.

Narrative

Normal takeoff from RWY XX at ZZZ. Climbing out around 800' MSL; student reduced power to maximum continuous (92% load) as required. Immediately after; the right engine began to surge; indicating between 75 and 85% load. Right hand ECU A and B fail caution indications appeared.I took the aircraft from the student; and informed ATC that we'd like to return to the field for 'a right engine indication'. Initially received RWY XX again; but requested [Runway] YY for better winds. Approved. Landed [Runway] YY; made the first left turn off. Regional jet behind was maybe five NM out for the same runway. To my knowledge; they did not receive a 'reduce to final' request or anything of the nature. They executed what sounded like on tower frequency to be an uneventful landing considering we were placed in front of them from tower.Cleared RWY YY; asked for a 180* turn around on the taxiway to diagnose and potentially continue; approved. Ran the ECU fail checklist; performed a satisfactory run up of both engines. ECU indications cleared. Requested another departure from runway YY at [Taxiway] 1.Received line up; then takeoff clearance. Once both throttles were in the takeoff/full forward position; I performed a normal engine gauge sweep; and noticed the right engine again was not producing acceptable takeoff power (left engine 98%; right engine around 80% and again surging).I rejected the takeoff and informed ATC; and made the next left turnoff ([Taxiway] 2). Tower asked for the RTO (Rejected Takeoff) reason; to which I replied 'similar engine indication; we'd like to return to the ramp; negative assistance.'Uneventful taxi back to the ramp.External factors: this was a flight lesson before a checkride; so there was a bit of 'let's try once more' for the sake of getting the customer to the checkride. Abnormal engine checklist usage; extinguished ECU indications; and a satisfactory run up lead to my decision to attempt one more takeoff.