Which version of Acrobat are you using? There should not be any change in the image quality when you import the image into Acrobat. How are you importing?
The only thing that could explain what you are seeing is a setting in the rendering options: Open up Acobat's Preferences, then go to the "Page Display" category and toggle the "Rendering" options:
Currently I'm using Acrobat Pro DC 2015.023.20056 on Mac OS X Sierra. I checked the Rendering setting under preferences and it matches with the screenshot that you have attached. I even tried turning off smooth image option but it didn't had any improvement in the image quality either. For replacing the image I click on "Edit PDF" option then select the image that I want to replace, Right-click and click on replace image.
I would try to toggle all of the rendering settings to see if any of them makes a difference. Can you provide your original PDF file and the image file you are using to replace the existing image?
I cannot share the original pdf due to our company's compliance policy restrictions. However, it applies to any image whichever you choose.
For testing purpose I've attached a sample pdf doc which contains an image, along with the same image used in pdf.
To recreate the issue, you can try replacing the image with the attached pdf and check the difference.
I observed the same quality loss issue while creating a new pdf from image through Acrobat. For pdf creation I'm using imagemagick script which doesn't suffer from the quality loss issue unlike Acrobat.
I think I know what's going on: I don't see a difference in the image quality, so that probably means that there is a setting that's different on your computer. Open up your Acrobat preferences, then go to the "Convert To PDF" category, select PNG as the format and then click on the "Edit Settings..." button. On the dialog that pops up, you can modify how a PNG image is processed when it's imported. The problem here is that Acrobat has to uncompress the PNG image data and then store it - for file size reasons - in a compressed format again. On this dialog, you can specify what compression mechanisms to use for different image types. This is what I use:
ZIP compression is lossless - and I don't see any change in the image quality - so I assume that your system is set up for JPEG compression with a low or medium quality setting. I am pretty sure that once you change this to ZIP, your image will come in looking just like the original. You can actually test with the Output Preview tool when you select the "Object Inspector":
When you compare the original and modified image, you should see the same information.