Occasionally I notice a shudder or hesitation in second gear under normal acceleration, never under hard acceleration. There's no pattern to it. The car has been well cared for, with 68k miles.

 

Is this an automatic?

 

It probably is torque converter shudder, if it's an automatic. The Honda dealer may have a PCM software update with different shift maps to help with the converter shudder.

When was the last time the transmission fluid was changed? Can also try several transmission fluid drain and fill with Honda DW-1 synthetic transmission fluid.

If there is damage to the transmission, software update and/or fluid change will probably not help much.

 

I had transmission shudder in second and third gear in my wife's 2007 Accord V6 5 speed AT with 56K miles. The shudder occurred only within the first 5 minutes of operation and cleared up after that. It occurred when it was first started in the morning or when she returned after work. . The Honda dealer tried to identify the problem with their diagnostic equipment and could not pinpoint the problem. I had them do a ATF drain and fill (with DW-1) as the service interval was about 2K away. It took about a week and the problem went away and has not returned after 6 weeks. I also had a problem with harsh shifting even after he first drain and fill. I had a second drain and fill performed with DW-1 ATF. This solved the harsh down shifts.