DA-40 Flight Instructor reported a dual failure of the Engine Control Unit (ECU) during cruise. Flight diverted and landed safely.

Narrative

My student and I were on a dual training flight; about 45-50 minutes in to the flight and conducting a steep spiral maneuver. About 3/4 of the way through our first turn in the maneuver; ECU A and ECU B fail annunciations appeared on the PFD (Primary Flight Display). I took controls from my student and called for the QRH. My student read the steps while I did them; the annunciations did not clear. When running the engine troubleshooting checklist; after increasing the load we experienced a recurring shudder from the engine as well as load % and RPM oscillation. At this point we were at a good gliding altitude from our steep spiral maneuver; somewhere in the 6-7 thousand feet range; and also pointed directly at ZZZ. I briefed to my student that we would divert to ZZZ; and enter straight in for Runway XX. There was another company aircraft in the pattern at ZZZ; I informed them over CTAF that we were experiencing engine issues and were coming in for Runway XX. They stated they would be out of our way and stay in the area to make sure we get to the ground safely. Considering how much altitude we had; I elected to leave the power lever at idle since every time I introduced power we experienced shaking from the engine; and I did not want to potentially aggravate any existing issue. As we approached ZZZ on a final for XX; I began doing some S-turns to help lose some altitude. I did not want to risk doing any turns away from the runway (like a right or left 360) in case I inadvertently lost too much altitude; and had to reintroduce power from our engine which seemed potentially unreliable. As I approached Runway XX I realized I had too much altitude to make a stable approach and landing; so I offset to a low left downwind for Runway XY. I was able to make a stable descent to Runway XY and land without any further issue. If I had to do it over again; I would have elected to first fly to the airport; steep spiral above it; then enter a left downwind for Runway XY. After Maintenance and Operations had been called; Maintenance came out to fix the aircraft. After a few hours they had wrapped up their work; said they did a few run ups and all Operations checks were good. On the ground; I briefed a plan with my student to ensure we operated the aircraft in a safe manner while ensuring our confidence in its mechanical ability. I told my student we would execute two laps in the pattern at ZZZ; and if those went well we would climb up to 3;500 ft in the close vicinity of ZZZ. As long as that went well; we would return to ZZZ1. My student and I did a preflight; then began to depart Runway XX. Takeoff roll and crosswind leg were uneventful. About halfway to 3/4 of the way through our downwind leg; an ECU A failure appeared on the PFD; followed by the same engine roughness from earlier. At this time I took controls from my student. Considering our position; I opted not to run any troubleshooting checklists; and focus on getting the aircraft on the runway safely. I made a short base; short final approach to Runway XX; and landed without issue. I again notified Maintenance and Operations. We had an instructor come and pick us up in a different aircraft and returned to ZZZ1 without further issue