Have you checked for Trouble Codes - you need a code reader and then find the socket on the car that it fits into / - might be a crank sensor - it would show as PO 335 on a code reader. Mike
I had almost exactly the same problem (Honda Accord 2.2 icdti 2007) - I have an excellent auto electrician - Mark in Stoke. He diagnosed the Voltage Controller ( a small part attached to the alternator) he changed it and no probs since then. Honda wanted £850 supply and fit - Mak charged £75 all in - Brilliant