check that the wire to the stop switch/contact doesn't have any breaks or vibration worn areas. If the cable arcs to earth it will stop the engine. Also check the clearance at the engine stop contacts-are they within arcing distance is anything loose that will allow the contacts to touch.
It is unlikely to be a sticking valve-you would hear the engine note change and the engine would not run smoothly.
If it starts and runs first time when cold then you have a very good engine look for the less obvious
cledlyn
June 2009