PA44 Flight Instructor reported engine shut down for training failed to air restart on several attempts; but eventually started on return to airport.

Narrative

We were in the training area and shut down the left engine for training purposes. During restart; the feathered engine; the student followed the CL (checklist) and gave a quick kick to start; it didn't start. Instructor asked him to wait for 20 sec and then hold the starter for 10 sec. did not start. We primed it and put the throttle to full forward and 10 sec of starter it didn't start again. Instructor waited for another 20 sec and with one more sec of prime and full throttle. Did not start with 10 sec starter. Instructor requested priority and started heading back to ZZZ. We secured the engine. On the way after one min instructor asked the student to run the CL again and we got it started on the 6th attempt. Instructor called to ATC and Dispatch and informed them. After completion of the mission instructor talked to maintenance to find out the reason. Maintenance mentioned that it could just be a vapor lock even at 5500 MSL. There was no injury or incident happened. We came back safe on the ground and squawked the airplane.