That symbol is the lane centering function that only activates while cruise control is engaged. It will deactivate when the Eyesight cameras can't identify lane markings well enough to keep you in the lane. While I'm not ruling out an issue with your vehicle, it is not uncommon for it to disengage regularly when the road conditions preclude it from knowing what to do. This will happen when the lane markings are not present, poorly painted/worn, or if there's bright sunlight glare on the road, precipitation, etc. Even some entrance and exit ramps will cause it to disengage when the lane markings disappear.
I drive through a lot of construction zones on a daily basis, and I just have to keep the lane centering function off because it just can't handle it. Also, roads with a lot of seal repairs (the zig-zag patches they put on surface cracks) can confuse the system.
It's annoying, but the technology just isn't developed enough for the computer to understand every possible condition on the road. So it just gives up and turns over control to the driver.