This is a coin-op machine? That probably doesn't really matter but it means the controls have been altered from a standard household model

If it stops on it's own and restarts 15-20 min later but only after you press start that sounds like the motor thermal safety is stopping it and then resetting, at which point it will allow the motor to run again.

Is the click you hear coming from down low, bottom left area?

Assuming it was converted to propane correctly and the person who did that job did not leave the vent disconnected internally or otherwise venting onto the motor I'd suspect a bad motor.

If the internal vent was disconnected from the blower housing during conversion and is blowing of leaking 200+ degree air onto the motor that can cause it to over heat and shut down. No harm is done as that is the function of the thermal safety on the motor but it shouldn't be doing it.

If it's under warranty still call it in. Most coin ops only have a 90 day warranty so do this quickly if it is that new.