I am trying to find the edges of the centered box in this image:

I have tried using a H
when resizing the image, the image is normally first blurred with a filter, e.g. Gaussian, in order to get rid of high frequencies. The fact that resized one works better is likely because your original image is somehow noisy.
Try blur the image first, e.g. with cv::GaussianBlur(src, target, Size(0,0), 1.5), then it should be equivalent to resizing. (It forgot the theory, if it does not work, try 3 and 6 as well)