I had been experiencing this problem for some 6 months. A Honda service crew tried to replicate it for an hour but the engine started every time. I started to doubt the sturdiness of the battery which looked OK from the outside. I called the NRMA - like the AA in the UK - and a battery specialist came to visit with sophisticated battery testing equipment. The engine was cranking well at the time. He found the 370 CCA battery shwoing a resting level of 240 and confirmed that if I had not used the car for a couple of days, it would fall down to a level where it might have problems cranking the engine. I replaced the abttery immediately - it was only 3.5 years old - and the problem has finally been resolved. Best of all I didn't even lose my radio pre-sets. The Honda is a Mark 2, MY2012.