DA40 Instructor pilot reported a fuel transfer problem resulting in diverting to another airport and landing safely at that airport.

Narrative

I was completing a check ride retraining flight with my student. We had departed ZZZ1 and were returning to ZZZ. We had established communications and radar contact with ZZZ Approach. ZZZ had instructed us to go to ZZZZZ to start the arrival. ATC also advised that they may need to re-sequence our approach if ZZZZZ didn't allow adequate spacing. As my student was completing the descent checklist; he initiated a fuel transfer for 3 minutes. Fuel indication was 12 on the main and 14 on the aux tank. This was the first transfer of the flight. We had departed ZZZ with a full aux tank. As my student completed the checklist; I noticed that the fuel transfer annunciation was not on. I monitored the annunciation and checked the quantity indications. They had fallen to 11 and 14 respectively. After noticing that the annunciation remained extinguished; I cycled the fuel pump switch. There was no fuel transfer annunciation. I then checked the Circuit Breaker (CB) panel and saw the fuel transfer breaker had popped. I then ran the QRH checklist and used the fuel valve to begin to balance the tanks. ZZZ2 was the nearest airport. I communicated with ATC my intentions to divert to ZZZ2 and that we were experiencing an issue with our fuel transfer pump. ATC was helpful in providing traffic in the area and our distance to the airport. ATC asked us to report on the ground that we had made it via the clearance phone number. As I was setting up for the airport; the fuel had balanced; and I returned the fuel valve to normal. I was set up for a 45 to the downwind for Runway XX; the current runway in use. I communicated my intentions on the CTAF; and landed #3 behind 2 other company aircraft. We landed and taxied to the ramp. Maintenance was already on site addressing an issue with Aircraft Y. Once the aircraft was secure; I called both the Maintenance Operations Manager and TRACON. I spoke with the supervisor at the TRACON. She was working on frequency at the time; and wanted to make sure that we made it to ZZZ2 safely. After discussing the issue with maintenance; I squawked the aircraft and got a ride back in the maintenance van.