C172 instructor reported an engine failure during landing while conducting flight training. The flight crew landed and required a tow off of the taxiway to the parking ramp.

Narrative

During the entire duration of the flight (up to the point of short final at our origin airport); there were no early tell-tale signs of power loss. Conditions were 25-35 Degrees C around our areas of training; mostly clear skies and fair winds. (They told me this after the engine died); But engine did not appear lose power at that time. During idle power and touchdown; landing appeared as normal but upon turning onto taxiway and crossing the edge of the runway; engine started to lose RPM and then after 5-10 seconds; the engine quit completely. Before it quit; the student noticed this as well; and attempted to add throttle as they assumed that not enough throttle was being applied to maintain engine above idle. We were able to cross over the hold-short lines with the remaining momentum of the aircraft; but just barely over. I attempted a restart by turning on the boost pump; mixture full rich; and throttle in 1/2 to build fuel flow; but failed to restart. We addressed ATC; and had airport ops tow us back to parking. My student told me after stopping past the runway that on short final; that he noticed a lack of power gain when throttle was applied. No one was injured and plane was grounded after securing. I initially suspected vapor lock as the conditions were warm; but this was before my student told me what they experienced while on short final. I suspect it to be fuel injector-related or fuel pump-related.