I have a 2009 Accord. Twice on long trips (~40 miles) in the rain, the car started missing badly, and the check engine light began blinking on and off. The first time, I pulled over and shut it off, restarted it, and everything was fine. A few weeks later, I took it for an oil change, and told the mechanic about it. He checked for codes, but there were none. The next time it happened (again on a rainy day on the same 40 mile route), I shut it off, turned it on, and drove straight to the dealer. He said it was 2.5 qts low on oil, and that could make it act that way. I check my oil regularly, so I was really surprised at that. It hasn’t happened again, but now I’m really obsessive about checking (and recording) oil. It’s always full, never low – except that twice, after the car has sat all day in cold weather, the dipstick was dry. I drove it home (a couple of miles), let it sit for an hour and checked the oil to find it full both times. I’m religious about changing the oil, so I doubt that there’s sludge in there… Ideas?
Sounds like the oil is pooling in the valve covers instead of draining down into the pan…
But a 2009 model can’t have that many miles on it (or time on it) to be sludged up…How many miles on this car? Perhaps the valve covers need to be removed to see if there is a problem with the oil draining as it’s supposed to…
He said it was 2.5 qts low on oil, and that could make it act that way.
We get lots of reports here about really weird things that people at dealer service departments say. This one is way up there among them. If rainy weather has a tendency to make your car run really poorly and your check engine light flashes this is pretty much always going to be a misfire from wet ignition components or similar. Did this dealer place scan for error codes? If so, what were they? They look like “P1234”
As for the occasional low reading on the dipstick. I’m pretty much at a loss there [edit], but Caddyman’s idea seems plausible.
The car has about 32K miles on it now - had 27K when problem occurred. I’ve attached a .pdf of the receipt from the dealer stating that there were no codes found, but that low oil could cause this. Sounded bogus to me, but what do I know? 
Where do I go for more help - I thought the Honda dealer would have the answer if anyone would!
Yes, the dealer should have the answers. And I doubt that they would mislead you since they are reimbursed for warranty work by the factory. You might try that fateful route the next time you have rain. Make sure you check the oil before you leave your home to ensure it is full.
I have… a number of times, in fact, with no issues.
When the dipstick was dry, did you turn it over and look at the backside? Did you reinsert it and make sure it was all the way in and check it again? The dipstick tube on a Honda 4 cylinder is curved and can wipe one side of it off.
The misfiring sound to me like it was caused by something in the engine compartment getting damp. Any of he high voltage compenents getting wet could cause this. I’ve never worked on your make/model/year, but I’d suspect any of these components if your car has them: Ignition coil, HV wire from coil to distributor, and plug wires. Any cracks in the insulating material of components, even tiny ones, could cause this. And they’d work fine when dry, but cause mis-firing in damp weather.
One time I had a VW Rabbit that would run fine as the day it was new except if I drove over a pool of water, when it would stop dead on the spot. After 15 minutes it would go again. Eventually, after a year or two – well, I’m a little dimwitted 
– I took all the high voltage components off and put them on the work bench and inspected them. I found a tiny almost impossible to see crack on the underside of the ceramic coil. housing. I put on a new coil and it never happened again.
If it was wet though, would shutting it off and restarting it fix (dry) it? My thought was that I “rebooted” some computer in there by shutting off and restarting…