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Firstly, I drive with one foot...

I'm having a similar issue with my 2006 Civic Hybrid that I bought new in 2006, and have about 140K miles on. Sudden acceleration loss, no warning lights display, no computer codes are thrown. Really scary situation. Drove car 36 miles over a mountain pass yesterday morning, no issues. Returning home, after driving only 5 miles, there is a freeway connector that goes up a steep hill and after climbing that and merging onto the other freeway, the car starts jerking, can't seem to "catch" to get the RPMs up. I immediately get off the freeway and drive surface streets for a mile or two, no issues. Get back on the freeway, and start to climb a hill and here it goes again. Rush hour traffic. I luckily find a turnout,I pull over, put it in park, and floor it and it maxes out a bit less than 3K RPMs. Turn the car off for a minute or two, back on, engine revs to about 4.5 (dealer says there is limiter that won't allow it to go higher in park so I hit the limit). This is the second time it has happened to me in exactly the same physical locations. 2 mechanics have been unable to duplicate the issue in a road test. Tonight the mechanic will take it home and have a scope attached to see if they can get it to happen.

This is a really dangerous situation and I'm not sure what to do if they can't locate the issue and fix it. Sure, I can get rid of the car but the thought of pawning the thing off to someone else who might get in an accident is something I'm not sure I could live with.

 
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So I know this is an old questions n but I had the same problem for a long time and Honda could not figure out what it was. I recently changed my fuel pump and the problem is completely gone! I hope this works for anyone still looking.

 
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I am having that same problem with a 2014 Honda Civic that I just bought used from a Honda dealer a week ago on May 9, 2020 . The car has 67,000 miles and it has a hesitation problem from a slow start in a parking lot where the engine won't go past idle even though i'm pushing down on the gas pedal , until I let off and press it again slowly . This is very dangerous for pulling out into traffic and I would think Honda would want to fix this problem before someone is seriously injured or killed .

 
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2 things come to mind:

Do you drive with 2 feet?
There are conditions in which engine computer will ignore what you are doing to the gas pedal because it detected the brake pedal is not completely released. (programming strategy to avoid unintended acceleration)

If the delay only happens like in the first few seconds after you start the engine and immediately put the shifter in D, that is likely normal as well. The CVT transmission is not the same as a traditional automatic trans. The delay allows time for the cvt trans to get fluid pumping and get itself ready to drive before it pays attention to the driver. Surely this strategy also helps avoid transmission damage.