[MT-2500]

Welcome to AF.
What engine and how many miles on tune up?
What is engine service and repair history?
Any aftermarket remote start or antitheft stuff?
Any check engine lights or security lights?
Does the engine crank over good when it acts up?
Does it no start when hot or cold or both?
Watch that security light for going off after the key on bulb check.
Your service department is right it needs to be caught in the act to find the problem.
When no start you need to check for lose of spark or lose of fuel pressure.

Outside of that check for stored or history codes and check the fuel pressure.