Quoted From bälon:
Sounds like a bad main relay. Pull it and test to make sure
Main relay’s don’t often do this, in fact they hardly ever do. If a main relay goes bad it normally causes a no start condition it’s not normal for it to just shut the car off.
It is however quite common for the electrical portion of the ignition switch to go bad on Hondas so you might want to try a little experiment. Try holding the key toward the ‘crank’ position just after you crank the engine, if the engine stays running while you do this but when you let go of the key it stalls this is the most likely suspect. You don’t need to replace the entire switch just the electrical portion.
If this doesn’t work you then need to follow the basic steps to find the cause of a no start, it just so happens I have a video.