Honda - Odyssey :: 2001 - Won't Start On Occasion - No CEL / Codes

I have a well-maintained 2001 Honda Odyssey EX with about 162k miles. It's had all of it's recommended maintenance at the recommended intervals. And until lately all of that maintenance was done at the dealership. Of note, the transmission was replaced by the dealer at around 100k miles. Other than fit-and-finish issues it runs great.

Over the past few months, I've had issues with it starting. The key will turn, everything "lights-up" as it should, I hear the engine crank normally, but it just won't start. I do this 2, 3, 4, 5 times over a few minutes and finally, it starts. When it does start it runs fine. Sometimes this happens several times in a single day. Sometimes it goes for 1-2 weeks without it happening at all. I've tried to make a note of when this occurs to see if there is a pattern. Unfortunately, I've not come across anything obvious. The engine can be cold or hot. Rainy weather, dry weather. (I opened the hood and sprayed it down with the hose, it started no problem at all.) I've paid attention for the "immobilizer" indicators and I don't see that either. No check engine light. No codes.

A friend suggested that when this occurs to sniff for uncombusted fuel in the exhaust -- I did not smell anything. I suppose this suggests that it's a fuel issue and not a spark issue. I've taken it to my trustworthy local mechanic, and they a) couldn't recreate the problem, and b) couldn't find anything wrong. For good measure, they removed and cleaned the throttle body, but that didn't work.