PA28 Flight Instructor with student reported the engine shut down as they prepared for takeoff. After restarting the engine the flight was continued with no further problems.

Narrative

At ZZZ around XA:30am; a student and I finished engine run-up checklist; including magneto check with no problem. Density altitude was about 7;000 feet and 12 minutes after holding short of runway; we were instructed to line up and wait on the runway. As we get on the centerline of the runway at power idle; the rpm drops below 300 RPM and dies. Considering the density altitude and the time we were holding short; I thought it was fouled spark plug issue; which is quite common. As we attempted to restart the engine; the Tower gave us the clearance for takeoff and we had to abort takeoff. After 3 attempts; the engine was successfully restarted. Smart action would have been going back to the run-up area and run the run-up checklist again or to cancel the flight and ask a mechanic. But since we were not at our primary airport and thunderstorm was forecasted within 2 hours; I made a decision to proceed with the flight and let the Tower know we are ready and took off. We came back to the primary airport; which is ZZZ1 with no problem.